There are a number of ways to integrate/connect a sub to your main speakers depending on the available connection options to the sub. There are also placement considerations to improve bass propagation as well as treating the room to ensure as close to flat LF response at your listening position.
Offhand, without really knowing much of your predicament, I'd start with the following before jumping into conclusion that a better sub may do the trick.
(1) If its a floor-firing sub, the designers voiced the sub in that postion to achieve the best results. So maybe altering the firing position may not be a good idea.
(2) You may want to re-position the sub at the center along a wall. Not in the corners to lessen the perceived boominess. Corner placements reinforce bass frequencies to make them sound more powerful but create room nodes that result in peaking and cancellations at different points in the room.
(3) Use a lower crossover point. There are some guidelines in setting the crossover points between the mains and the sub. But rather than go into details, suffice it to say that the best crossover point would be one where the mains and the sub frequency response curves are at -3db in order to eliminate peaking that usually happens when both the sub and the mains are delivering the same set of frequencies. Your sub and speaker's technical spec sheet should indicate the -3db and -6db points. If not, you may have to use an SPL meter with a sweep of LF from a test CD. Or, just trust your ears.
(4) I agree it would be a waste to set the Axioms to SMALL when they can rightfully be set to LARGE. But you said your Yamaha doesn't have bass management. The fact that you can set to either large or small does indicate it has minimal bass management to route the bass frequencies to the sub when set to SMALL, right? If so, you may have little choice but to go SMALL in order that the mains and sub don't deliver the same set of LF and thus preclude bass peaking that most likely occurs when you perceive this boominess. If you set them to LARGE, the sub must be set to a crossover point at the lowest LF limit of your main, say 50hz or 40Hz. That way, the sub complements the mains by an octave of bass frequencies lower. But since, your sub can only go to 75hz as its lowest crossover point, you're effectively augmenting the main speakers' 75hz and below, thus you get a perceived boominess.
If i may suggest, try borrowing a parametric equalizer where you can set the center frequencies at 75hz and some lower frequencies so you can do some attenuation at the points where the sub and the main share LF signals. That way you can tame the apparent peaks. The equalizer should sit between your reciever and the sub. Alternatively a 31 band 1/3 octave graphic equalizer with center frequencies in the relevant low frequencies will do as well. If it works to your liking, then you can purchase one that won't cost more than $300, if not mistaken.
If not, then a better sub is it. One with a variable crossover knob than can go down to 40Hz. That way, the sub will deliver only those LF your mains set to LARGE cannot. One with a variable NOTCH filter that can tame room peaks. Otherwise, without these, I would caution you that if your room accoustics are conducive to LF peaking where you get boominess at your listening positions, using a more expensive sub in the same position with the same listening position will just create the same LF peaking. This time, more expensively.
There's an excellent article in this site about Bass Traps you may want to read before attempting to get a more expensive sub. I think it's in the room accoustics section. But do try the equalizer remedy. Just me 2 cents.
