This is the crux of it, I'm sure. May's red lines painted the UK negotiating team into a corner before discussions had started. Corbyn could approach the EU afresh, without those red lines in place and renegotiate in good faith. I believe the EU would be receptive to that (all talk about this being the only deal in town presupposes May's red lines remain in place).
Assuming, then, that a more sensible and workable Leave deal could be worked out, it would be right to put this before the country. It really is immaterial to the EU whether Corbyn, or his party, gets behind the deal or promotes 'Remain' instead. What matters is that the negotiations would be done in good faith, with the clear intention to get the best deal and the most constructive Brexit arrangement, then put that to the people. Depending on what the final deal looked like, the government position could be 'this is a great deal, we should take it' or 'this is the best we can expect, but it's not as good as what we have now so we recommend not taking it'. Either position, if honestly presented, should not prejudice any renegotiation with the EU, as far as I can see.