OP, if you really want a small bass module, get
this 6.5" Tang Band and put it in an 8" x 8" x 12" box (internal dimensions). Add a 1.5" dia x 7 3/4" long tube, and you'll end up with a tiny, well-controlled unit with an F3 around 34Hz.
Or, since they're cheap and most 4-ohm stable mono or bridgeable amps would be overkill, a dual driver option might make more sense. Two of those drivers opposed in a 10"x12"x12" enclosure with a 1.5" dia x 3 1/3" length port would have a similar F3 without much increase in size, but you could wire it in series for an 8 ohm load. (Just bear in mind that the wattage gets divided between the drivers in series, so a 100 watt amp becomes a 50 watt amp.)
Or a pair of
these 4.5" drivers in a box with internal dimensions of 6.5"x6.5"x10" and add two 0.75" dia x 7 1/3" length ports, and you'll actually have response pretty close to the single 6.5" driver option I suggested first -- just with a few dB less output. Unfortunately, this config will probably put you over the $200 mark once you buy an amp and all the cabinet components.
In any case, there's one thing all those drivers offer that your current one doesn't, which is a set of published Thiele-Small parameters.