Which component to upgrade to improve bass control?

You are missing the point completely.

A DSP will have far greater benefits than downsides. Lazy audiophiles hide behind "oh adding a component in the signal chain is devastating" OR "converting AD then back DA is devastating"

But you need a calibrated measurement microphone using REW on a computer. And there is a steep learning curve.

That is what drive 90% of audiophiles away.. it is hard.. oh i just put a spring or cement block under the component.. that is easier.. even a 10 year can do that..

Ok i have probably offended some people but in my system I could get RID of components when adding a miniDSP 2x4 HD. Removed a passive preamp, and a DAC. So win win.
And digital in and only a DA conversation..
It is only the TT that uses the analog in and reap the benefits of the DSP implement rumble filter + room correction + crossover + other benefits that is greater than lazy purist that is justify their approach that they are in the analog domain the whole signal chain.. the same people are hunting after the right component/cement block/spring. 😉🤣

You can grow with your external DSP when later on getting a subwoofer.. Get a subwoofer without DSP cheaper (it is in the wrong location in your system and is limiting what you can use it for..)

My external DSP are doing seven different sound enhancing jobs that can’t a built in DSP in a sub do..

So those seven tasks will beat any spring or cement block in sound quality improvement any day. Plus you are able to CUSTOMIZE the sound the way YOU like it. Plus you can have four different presets depending on mood, album or whatever.

You will be knowing what your system are doing in the measurements and exactly where the weaknesses there is and what to target plus fix some of your room issues. There is so much to learn and to gain but I will stop here.

I do not know what is harder.. adding vibration control and swapping in and out components (in retrospective) all your life or learn and evolve. (Just trying to be brutally honest)

Keep on listening! 😍🎶

You look at it is n the wrong way. Maybe because you lack the knowledge what a miniDSP is doing for you.🙄

When saying:

very much doubt the DAC in a $250 device is going to equal my Aqua. 

If we take one of the many things miniDSP is able to do. PEQ for example, so when you have measured your listening space at your listening position with your calibrated MIC ($100).💰
And knocked down peaks and the biggest problems of your room and downloaded the generated PEQ file to the miniDSP so it flatten and solve the biggest issues in sound quality at your listening position.🎶

Then the truth is that there is NO Aqua or ANY external DSP no matter the price that is going to equal the sound quality at your listening position as the miniDSP using PEQ.🥇

You are trapped in a false belief that oh only that if I got a better this or that. As I tried to tell you can keep doing just that whole your life without getting anywhere. But that is maybe something you enjoy more than sound quality? So please go on.🔄

Another point is, if your problem is "bass blom". And you look at the basics for what type of principal your speaker is designed with. In this case a bass reflex ported construction. That is time smearing and a bloomy design in it self..🌼
So you say dear Mr bass reflex do not be what you are and you should try to be like a sealed or OB construction please.. because you are so gorgeous and I want that you please me.🧙‍♂️

You need to look at what technology you are using. And those speakers are probably not for you when they do not please you. And do not try to make them things that they are not designed for. 🤔

Perhaps you can explain why some DSP units include a DAC. What's the point? 

DAC = Digital to Analog Conversation
ADC = Analog to Digital Conversation
For example the miniDSP 2x4HD:
It has a analog input there you can connect the LP and it does a ADC and in the digital domain all the magic then back to analog with the DAC.

But it has several digital inputs there it does the all the magic and then to analog with DAC.

Here is some of the whys/points when this model has 4 analog outputs that you can use however you want.. 

One example is you can choose to use output 1 and 2 as left and right that goes to the power amplifier to your bookshelfs. The other two 3 and 4 can be left and right for your subwoofer power amplifier/s.

So as you see there is four outputs in this case if you "only" got a digital out from the DSP and then connected to your standard standalone DAC that usually only give you two analog outputs. What is the point with that? Rather useless in my opinion. ;)
Then you can "only" do room correction.

In the miniDSP case the two left and right 3 and 4 output is treated individual so if you have the right subwoofer on a different distances than the left one then you can time align them separately so they are aligned with the bookshelfs.

You can implement where the x-over should be for the subwoofers and bookshelves independently and offload the power amplifiers. 

And so on and on there is so many configuration and use cases..

Now we are moving in the right direction..

When you have sloppy bass with your bookshelf of the reasons I tried to point out previous.

How does the logic work by still playing with those sloppy bass makers and also add subwoofer/s..

Will they stop to produce sloppy bass? I do not think so.. Maybe the subwoofer/s will mask it if they play a little bit louder..

(A fix if you get subwoofer/s is (again the DSP) if you measure where in Hz you have your sloppiness and if we are lucky it is the bass reflex port that is cousing the sloppy bass and for example it is maybe between 40 and 60 Hz. Then set up the x-over in the DSP that feeds the powe amps is above 60 Hz so that your bookshelfs is not playing anything below 60 Hz.)

Regarding that maybe try to plug those bass reflex holes quick and free test. It will not play that low but maybe some sloppyness will disappear.🤔