Which Icon 300B amp do you have? All the ones I'm seeing from a quick search look like they are push-pull. If you have the one with four 300Bs and four 6NS7s, that has the tube complement and output transformer size typical for a push-pull amp.
The Forte III has a few dips to around 4 ohms in the bass frequencies, so possibly using the 4 ohm taps could help even out the sound. How does the bottom end response change if you go from 0dB to 6dB of feedback on your amp? Increasing feedback will reduce the tendency of the amp's output to wander as the speaker impedance changes.
As far as 300Bs and no bass, there are definitely a lot of output transformers on the market for 300B amps that aren't so great on the bottom end. Furthermore these amps have a lower damping factor and that can interact a bit with bass reflex boxes as well.