New Klipsch Forte III’s

I have a pair of Forte III's in a 2nd system and I agree, the Forte III's don't produce enough bass as they only go down to 38Hz.  I added a HSU ULS-15MK2 sub and the sound is perfect, filling in that low foundation and improving every aspect of the entire range. I don't think you'll get that much improvement from break-in alone.

You could bi-amp from your BAT pre using the RCAs to the parasound and the XLR to a nice VK-220/225 amp. Not only would you have more power overall but the output via XLR is like 3db greater giving you a nice bump to the bass! I briefly heard the Forte III in a showroom setting and it had very nice low-end output. 

When I first got my Forte IIIs, I had them connected to a Vincent SV-500 integrated amp.  Had them placed very close to the wall, somewhat close to corners.  No subwoofer.  They were sending earthquake-like bass all over the house -- it was incredible!  I've changed my setup a lot since then, including going to much smaller speakers and a different amp, but that bass was memorable!  When I switched to tube amp, the bass pretty much went away.  I'd say blame the room, blame the amp if you're not getting good bass.  No experience with the A21 myself, though.

@redwoodaudio  Interesting. I have to say, I'm using a tube amp with my Forte III's and I can't completely rule out that the less-than-optimal bass is due to the tubes/transformers which may be challenged. In any event, the HSU completely filled n what I was missing and the mids/highs are glorious.