So May's deal really is the only deal we could join EFTA post leaving.
Not exactly sure what you are saying here.
May's deal is the only deal on the table agreed by both the UK and the EU for the withdrawal of the UK from the EU and the arrangements for the immediate period post-29th March (so called transitional period) during which a final deal between the EU ad the UK is expected to be negotiated and agreed (based on the aspirational political statement).
Joining EFTA cannot be the withdrawal arrangement for obvious reasons that I have stated previously. The UK cold propose that is becomes a member of EFTA for the final arrangement, but cannot do this unilaterally - firstly (and obviously the EFTA 4 would need to agree this) but secondly the EU would need to be convinced that the arrangement satisfied the internationally legally binding agreement of the withdrawal agreement - specifically on Northern Ireland.
And of course finally EFTA membership would need to be politically acceptable to the government, parliament and in the country at large. As I've pointed out previously I'd imagine that a proposed EFTA permanent solution would rank very highest on the 'betrayal' scale - bringing together brexiteers who would feel betrayed that this was 'Brexit in name only' (requiring freedom of movement, EJC involvement, payments to the EU etc etc), plus also remainers who would feel that remain would have won the referendum, if the choice was EU membership or EU membership-lite (i.e. EFTA).
Plus I'm not convinced it would be considered politically or democratically acceptable to join EFTA without a specific referendum on membership.
So, yes EFTA membership is a possibility, but it is fraught with complexities, so it isn't a simple solution.