What did I hear?

or you can swap the rotel for an arcam delta 120 same price secondhand better realism and weight for sure. rotels are too bright for some speakers

1.what tubes are in your line stage preamp?
i know the current version uses 2 12at7 tubes.swapping preamp tubes is a fantastic way to voice the amp the way you like.more weight? try 70's made nos blackburn mullard 12at7's (100-150$)they have huge bass ,slightly lowered highs and sound very smooth full and weighty without losing clarity or definition. 
2. schiit loki (180$)eq will help you finetune the tone to your taste
3.ifi itube2 tube buffer has extra bass (but in an audiophile way not like on bose stuff) 

Oh no, did I fart?

I recently auditioned $5000 in new Rotel equipment, including a 200 wpc amp with matching preamp and CD player on current B&W 804 speaker, because I reasoned that  the sound would closely resemble my older 803's.  It was truly horrible, both brittle and obnoxious.  Even the salesman mentioned that it would not be good for longer listening sessions.  I thought for a total of over $10,000 it would be at least tolerable. I took my own CD's, because I knew them.  They sounded fie with the Mac gear he had, but for the money, i kept my old stuff. (Audire and Bryston)

I sold McIntosh it is well built and meters are real nice looking build quality for the moneytoo many avaerage parts all $4 wima caps where much higher grade capacitors could be used 
Pass labs for similar money beats them Soundly  .quicksilver decent for a lower priced preamplifier . In today’s market 
unless doing lots of mods which I do to get 3 x the performance 
per dollar then $20k on electronics is about average in today’s market..as a former dealers cables are by far the biggest markup 
up to 6-1, speakers,and electronics not even 25% goes into the cost ,the rest overhead and dealer markup. That is why I personally seek out a used product and with speakers rebuild the Xover with all quality name brand parts not chinese,
electronics same thing  night and day difference in sound.
and your rca, Connectors,and speaker terminals 85% are cheap gold over brass.i changed all To High Quality Gold Over high quality Copper ,sonicly noticably better 4x better conductor 
same with fuses stock steel fuses a Huge botttle neck just look 
up metals resistance index a 6-1 ratio Silver -Copper fuse vs steel
buzz fusev.everythung goes through the fusethat much resistance 
hue bottle neck and loss of low level detail. One thing I Highly
recommened for the moment is Furutechs Nano liquid Silver and Gold particles suspended in a specific oil, coatevery metal surface 
I even do tube pins a very noticable difference takes several weeeks to fully embed in the pours of the metal a very cost effective improvement.it will sound a bit bright for the 1st 24 hours 
but just gets better silver paste not even close. I am testing a 
new product that is much more expensive but even better.
once offficially out I will let others know .thats my opinion through 
40 years of experiences.

Basically if it sounds better to you it is better. The Rotel is a decent budget amp but a better amp will give you more of everything. Frequency extension, weight, tone, midrange density. The Mac is obviously a great example of a very good amp is a very good amp regardless of age.

You might try an upgrade with some new tubes in the preamp.

v7b9b13, with a really good post asking some of my favorite questions! Trying to make sense of it all:
   

It was a dramatically different sound. It was, for lack of a better word, tremendously more robust. Not loud, but large. Deeper bass. Rounder tone, everything had more weight and presence. Not in a distorted or in-your-face way, just, somehow... livelier. Bigger.

This happens a lot. Some components, actually I think the vast majority, offer up thin gruel, a skeletal, ghostly, not quite there sound where leading transients are hyped, along with the top end, probably because the average audiophile confuses etch and grain with detail. When what you really should want is called palpable presence, what Michael Fremer is talking about when he says "there's more there there". Its good you appreciate the livelier, bigger sound. This will serve you well.

Same by the way goes for not just amps but everything else. Synergistic Research in particular is known for superior weight and presence, yet while still being free from fatiguing grain and glare. SR is known for their high prices because they have been making some of the best in the world for so long now, and the best in the world costs a fortune. But because they have been making the best for so long there's a LOT of really good used SR out there for cheap. Earlier this year I bought what were 15 years ago $8k Element CTS speaker cables, some of the best in the world at the time. And still freaking good today, I am here to say. Only now, less than $2k. Their industry standard 

In my book the sound you describe is exactly what you want to be looking for. It can be found, regardless of budget, because regardless of price there are always things that sound this way much more compared to everything else at whatever price level you are at.

I was actually surprised because the MA-5100 is a 45 watt amp, but it seemed to wake the Ohm Walsh Talls up more than the Rotel, which is (I think) 120 watts.

Its a well known fact that not all watts are created equal. Tube watts in particular tend to subjectively play as loud and with as much authority as twice as many solid state watts. You can dive down the rabbit hole of tech specs if you want, and if you dive deep and long enough even make sense of it all. Quite honestly having done all that, and years ago, this is hardly worth it. What works just as well and a whole lot faster is to just pay attention to comments and reviews and use those to winnow down what is worth auditioning.

I know the standard approach to stuff like this is to listen to everything and go with what your ears say, but I don't really have the budget

Pro tip: no one does! Here is where we separate the men from the boys. The boys will tell you what you said. Men see that as a waste of time and money.

You can't listen to everything. No one can. Its literally impossible! 

What you can do though is narrow everything down to a few to several components in each category that fall within your budget.

Now this is where we really separate the men from the boys. What you need much more than anything else is a really nicely balanced and fully complete system. That means one or more source components, amp, speakers, and interconnect, speaker cables and power cords. You need all of these, regardless of how big or small your budget. Skimping on any one creates the weak link that brings the whole system down.

Do this and you will be shocked how fast an incredibly complex and daunting task becomes child's play: Take your budget, whatever it is. Divide it equally by all the components you need- source(s), amp, speakers, wire. That's 20-25% of your budget for each.

Unlike all the other advice you will get I have actually done this and more than once and know how well it works. It worked phenomenally well for the $1200 total cost system I put together for a relative as the $2500 system I did for a friend. Its what I have done over the years as my system has grown from about $5k to ten to twenty times that. 

Budgeting like this forces you to narrow your choices down. It is however a guideline not a Commandment. Don't get hung up on it. Use it as a tool to save you from running like a hamster on the wheel, always running, never getting there.

It was pretty fun!!  :) :) :)

I wouldn't take that as the fabled Mac sound (which is totally different with their tube amps FWIW) but its not a stretch at all to discover that a better amp can sound better than one that isn't as good :)
Welcome to the world of high end audio, where you can hear differences!