cast aside by a vendor team

[DirtyDog]

Forget the vendor, you are probably there because the client insisted and it is very unlikely they will ever want you involved if they can help it.
BUT, usually engagement with clientco will be on an individual basis and it is this interaction I would concentrate on, nothing too much trouble, volunteer for actions even if not your core work, build up some contacts. I wouldn't slag off vendor to them but don't defend them at all either, a raised eyebrow says a lot...
There are NO guarantees but seen plenty who then transfer to client after vendor bins the role at earliest opportunity.

This.

It's great fun when you get the chance to move from working with the vendor to working with the client I've done it before - having spent ages being ignored when I flagged something with the consultancy which was poor (essentially being told to keep quiet because the client hadn't spotted it and was about to sign it off), I then had the chance to move to the client to review the acceptance criteria.