Which component to upgrade to improve bass control?

Hello,
besides the obvious of a better preamp and DAC. You need the Puritan PSM156 power conditioner. I would upgrade the power cord to the unit. This will cost $3300 total for the PSM156 and the Puritan ultimate XX. This is a no brainer. The next thing is your power cords. Make sure your amp can breath. I am going to recommend the Nordost Frey power cord. This will really help get better bass. If you can swing it go to the TYR 2. The gauge and the way it is made gives unbelievable control over the bass. If you live near the Chicagoland area this store will let you try before you buy:
https://holmaudio.com/
All of this helps the sound of the whole system. Plus, For another $275 you can add the Ground Master City to the Puritan for dead black noise floor. And it’s all plug and play. I hope this helps. 

Good footers for your speakers will decouple the speakers from the room. You will get crisp bass and way smoother mids and highs.

This comment stunned me. Maybe it's something huge that I overlooked but I thought that the bass waves being produced by the woofers and being amplified by the room were not something that could be neutralized by decoupling. If I'm wrong about this, I'd like to know, but it seems like something to do only *after* major problems involving the room had been addressed.

The proposal by hshifi — a better preamp, DAC, plus power conditioner, power cords, and a ground master — sound like throwing quite a lot of money at a much more fundamental problem. I'd bet an amount equal to their full cost that they would not help the issues you describe.

Your options are limited by the intrinsic acoustics of your room.  Regardless of the kind of room you have (dedicated or not) there will be peaks and valleys in the bass response.  Before making any purchases you might want to try a free/easy setup tweak before evaluating the more expensive option that may/may not work in your situation.  Using an RTA or SPL (can purchase apps for iPhone as well) you want to focus on the region 25-250Hz to find a position(s) where you get the most even bass response. That is where you want your listening position to be.  It is NOT about where you get the most bass.  Check out the link below:

https://www.psaudio.com/copper/article/location-location-location/

Good luck!
Gorm

Bass at the listening place is controlled through dsp. Look at Dirac as mentioned or a simple Paradigm (Anthem) ARC processor (0,5K) between your transport and DAC. When you've become more knowledgable you can move up the dsp cchain. Opens up to the best sound.

I agree with @gormdane.  I was also faced with bass issues, even after room treatments (that I needed anyway).  For background, I have a 2 channel setup with a sub and a 7.1 home theater setup in the same room so my listening spot for 2 ch. is relatively fixed (distance to TV).
After measuring the acoustics using RWE and a calibrated mic, i used Roon's DSP to tweak the bass frequencies.  (Taming a bump at 43hz had the best result.  That bump was caused by room dimensions...something I confirmed by using an online calculator.)  That improved the sound for digital however still let me with the same issues for my analog (turntable) listening.
My dealer suggested JL Audio's CR-1, an active x-over.  Before doing anything else, I verified that the bump at 43hz was present with and without the subwoofer active.  That allowed me to eliminate the subwoofer as a contributor to the bump.  The room calculations helped me confirm that it wasn't my speakers, etc.

Long story short, I was able to borrow a sample from my dealer and test it at home.  Using RWE I was able to adjust the cross-over settings and slope to tame the bass at 43 hz...still a slight bump, however much lower than w/out the CR-1.  The bass was tigher and the overall sound was much better.
I now listen to both digital (with no DSP) and analog with the CR-1 installed in my system. 

If your integrated allows you to send a signal out to a pre-process and has a power amp in, you might want to try the CR-1 if you can get a loaner.