The base that is removed must be the one which was facing the BG that inflicted the most hits. Assuming that both BGs inflicted the same number of hits, the loser decides which base to remove. This means that either the base facing the HF or the LH must be removed. Whichever base is removed must then be replaced by the overlapping base. But this creates a gap in the front rank which must be filled by sliding a base sideways (owning player's choice).
I agree with this entirely, however your last statement:
In either case, this will leave one enemy BG no longer in contact. Them's the breaks.
I don't think is correct.
The enemy BG no longer in contact is simply moved to remian in contact.
The next melee round will be 1 base versus the HF and 1 base versus the LH and the cav will still be fighting in two directions.