If your sub does not offer an LFE input (bypassing the internal low pass filter) you're losing a.lot of flexibility. Unfortunately, an LR4 high pass on the mains and BW2 low pass on the sub just won't add up perfectly. The problem is not just right at the crossover frequency but mostly above it due to the non-matching phase shift.
One approach would be to not use Subwoofer Bypass Mode, but to select a crossover frequency at least one octave lower than your subwoofer's upper frequency limit. If you cannot set the internal low pass filter any higher than e.g. 120 Hz, this would imply a crossover frequency <= 60 Hz, which might or might not be suitable for your speakers (which also form a natural high pass, usually 12 dB/Oct or 24 dB/Oct depending on if they are closed or vented designs.
The other option I see is to enable SBM, but in this case you'll have to tinker with subwoofer level, crossover frequency and delay (and potentially the phase switch) to come as close as possible to a response with as little dips as possible. This is best done using a mic and measuring software like REW. There's no need to be afraid of extra peaks, since RoomFit will be able to tame these later. It might be doable, but it's potentially a lot more hassle.
Go figure.