How far can room treatments solve boomy bass?

They can make it better at least. How much they can do depends on the extent of the problems.

Depends on how you address the problem. If you take measurements and do your homework, you'll be surprised. If you just start buying soft stuff, it's guesswork.

Room treatments in a room too small for the speakers is not the answer. Speakers that are to large for the room is one of the biggest problems in audio. I'm a firm believer in room treatments, but it wont fix your problem.

Bass traps in the corners of the room can do quite a bit to even out bass response. Even when you go to a bigger room, tube traps will be a help. Treat at least one end of the room (traps in each corner) and preferrably all four.

To with the biggest traps you can get away with--there is no substitute for thickness/mass when it comes to bass trapping (the exception would be "active" bass traps which use a speaker that cancels bass). With the round bass traps, like the ASC tube traps, I like the 16" models.

While room treatments are very important, I think the system used is just as, if not more important, in determining the kind of sound you will hear. Every one I think would agree to try "bass traps" in the corners and to get the speakers off the floor. Also reduce bass reflection from the floor with some sound absorbing material like a rug.
Then invest your entire retirement money along with any other holdings in a brand new, top of the line, state of the art system, and you will be all set.