I’ve found that most of the attractive ex INV fares recently have prohibited the usual <24 hour connection and insist on <12 hours which prevents an overnight stop and therefore baggage retrieval at LHR & a B2B at INV. It also prevents getting the day flights back from JFK/BOS which are my preferred options.

Reports suggest a wait of up to 3-4 hours for bags. Understandably you are their lowest priority. Have you considered HBO for return leg? You should be fine with 2 bags each at the larger carry on dimensions in CW/F which should suffice for a city break. Obviously you have to be mindful of liquid limits.