More watts or better power ?

Do you feel that the sound from the speakers is thin?  Especially at moderate volume?  If your sound is lacking weight, then an amp upgrade would make sense.  But this sill be very obvious.  

Those are very good speakers.  You can change them but you risk upsetting the dynamics of the system and creating a cascade of issues.  

It sounds like you don't have any line conditioning in place and that is probably something worth looking at.  Furman makes nice products.  I think for the money, Puritan might be the best on the market.  A PSM 136 is not crazy expensive ($1600) and will do a lot to improve sound and comes with a pretty good power cord.  

Are you using the stock tubes in the BHK or have your rolled in NOS tubes?  That will have a shockingly large impact and be at most ~$250.  

Those would be the places I would start.  

It sounds like you have the itch to upgrade not because you need to but you kind of want to. With that, it is more pressure testing each component and finding the weakest link in the chain.  You have a great system that is better than many so you can stand pat.  

And incidentally, what is the old saying about opinions?

To me, lack of a conditioner is first.  I legit think that will help reduce your noise floor and expand your soundstage.  Doesn't need to be crazy expensive to get the big benefit.   A Panamax or Furman will get you there while some of the higher end units will deliver incremental benefit.  I would spend less than $2K if I were you.  And incidentally, just because your amp won't benefit from a conditioner, doesn't mean your other components won't.  DACs and phono stages may not be high current, but the circuits are delicate and small variations can impact sound.  

Second, your DAC is very good for the money but, improvement can be had.  I think stepping up to a better DAC will give you a leap forward in terms of resolution and image.  I have a few customers who have that DAC and side-by-side comparisons with others have delivered surprising results.  

Third, cables are worth considering.  They can be borrowed for a test. ICs, power cables and speaker cables can make a difference.  Which has the biggest impact will vary from system to system.  In my main system, I upgraded from a modest pair of Kimber Kable speaker cables to Audioquest Robin Hood and it was like I got a new component.  It was huge.  In my other system, the same exchange made basically no difference.  The swap from Kimber Tonik to Audioquest Water was big.  Switch from Water to Fire was minimal.  You get my point. 

I have heard some extraordinary changes because of cables.  Both good and bad.  I get a lot of cable trades and some very expensive cables have had shockingly bad impacts on my system and some modest priced cables have been surprisingly good.  Borrow some and see if you like it.  Keep an open mind in both directions.  Expensive does not mean better.  

Your preamp, amp and your speakers are all very good.  I can recommend better but I am not sure you will get a big gain without spending, and I don't mean the $3-4K it would take to trade up to a PS Audio BHK 250.  Simply adding power can help with many speakers, but I am thinking that is not the case with those speakers.  I would focus on quality and PS Audio, Pass and Sonus Faber are very high quality. 

Incidentally, no, I don't think your system is mid-fi.   If you want to spend $10K+ for any of those components, yes, you will see some gains.  There may be some diamonds to be found a lower prices but not obvious ones that are better to me.  

Hope this helps and good luck