Which component to upgrade to improve bass control?

Mo’ bigga speaka wya!
20’ runs? Bi-wire if you can. Otherwise double run w/stacked nanners. Made a big diff years ago w/the low impedance highly reactive subs I had at the time. 
My $0.02. Tony

You don't say why subs and room treatment are out. I have a friend who was in a similar position to you in a square room (the worst) with all hard surfaces and his expensive kit sounded horrible, I don't know how else to describe it, certainly brought no pleasure to anybody who heard it. I asked him what he intended doing. A local outlet had convinced him to buy a new and very expensive cartridge. I explained that he would not be able to hear what this cartridge could do in his poor room because the fine detail and better overall performance would be obscured. 

To keep this short: I brought in some big rolls of rock wool and placed them where I considered they would help the most. The change was huge and the mood of he and his wife picked up noticeably. The temporary stuff was removed and he later installed some smart looking absorbers and traps. If you simply can't have any panels which need not be permanently fixed then consider a multi-sub approach.

My same friend now with a new outlook listened carefully when I explained what he could achieve with a DBA. I built 3 simple sealed boxes with an 8" driver in each. I posted something about this recently on another thread. The boxes were made tall with a small footprint, not much bigger than the 8" speaker. One sub was used to support a nice pot plant, another to support a reading lamp and the third as a coffee table. They fitted very easily into the room and were hardly noticed.

You may wonder what a 'little' 8" driver can do. Well there are 3 of them and they serve to randomise the nodes, filling in the nulls and taming down the peaks. The performance of the whole system including midrange and tops improves beyond what seems logical. I very strongly recommend you consider this.

Other posters have wisely suggested a DBA and I agree but there remains the issue of overly long decay without the correct type of absorption.  This leads me to the popular idea that DSP can fix this. It can't fix it. It can't fix it because it can't reduce the long decay of some or all frequencies. How can it? It can reduce the peaks, sure, but only the amplitude not the length of reverb. With partial nulls it can't boost those frequencies by for example 15dB, the amp can't provide that amount of clean power and the speaker's voice coil would melt. Anybody doubt that statement then just calculate for yourself: you need to double the amps output to gain 3dB. If you started with a 50W amp and double it 5 times you will need ... 1600W !$%#

What about a total null which means zero information (music)? Any power driven to the null frequency will just cancel with the same power. The multi-sub system provides many more peaks and nulls but they are now less less severe with more informative bass as a result.

I know that after this post you will still receive advice to use EQ or DSP  These are and always will be a band-aid. They may help when the room is properly treated where only small boost or reduction is required. Resist the urge :-)

Hey stuartk...

I haven't read all the responses, however, my solution to great bass in a small room was placing a pair of subwoofers BENEATH my monitors, using IsoAcoustic isolation between monitors and subs.  Given your budget, the appropriate size and quality of good subs should be within your reach.  And, music lovers, a small investment in a $20-30 Laser Distance Measure (ruler) is vital to great system's loudspeaker positioning...all distances can be easily locked-in precisely, including important fore-aft rake adjustments for time-alignments.  You'll be amazed how rewarding precision will make to your system.  
Good luck, stuartk and More Peace, Pinthrift

@gp4jesus:

Speaker cables are not biwired but are double runs.

@lemonhaze:

My room is long rectangle, not square. In fact, I've already decided that multiple subs will indeed be my approach in our next house, where/when I can have a dedicated room for audio. Due to arrangement of furniture and other aspects of decor, it's just not practical currently. Nor are panels, traps, etc. 

@tvad:

I'd assumed pods would be located under stands but millercarbon clarified for me that they should go directly under monitors. Here in the Sierra foothills, we have earthquakes from time to time and I simply don't trust that my Silverlines would remain perched atop the pods, given a good shaking. At this point, I cannot afford to replace them, so I prefer to play it safe. 

@pinthrift:

I tried isoacoustic footers under components and they didn't seem to do much at all but using them as the "filling", sandwiched between monitors and subs is not one I've encountered before. 

My living room is good-sized and is separated by diningroom by a half-height wall. Both have 10 foot ceilings-- it's not a small space, by any stretch. 

@geof3:

I'm not opposed to dsp but when I read descriptions of using it, it sounds a bit intimidating. 

@bigaud:

Thanks for your input. The speaker cables are double runs, for whatever that's worth. Not sure whether that compensates for resistance. 

 

Less resistance means greater damping factor (control).

Damping factor has very little to do with damping of the membrane (in spite of the name).

Well, we must all bow to practicality.

Given the fires in CA, the idea of moving back east is very appealing.

We lived in Maine for 9 years and loved it. 

We started looking at real estate listings and talked about having a house built back there but at a certain point were compelled to face the truth  that we've reached a point where age-related considerations render such a move impractical-- perhaps even foolhardy. If one of us were to become seriosuly ill, living on the opposite coast from all family members would not be an asset.