Hired for big budget recording session for independent band's album - No contracts involved. What does that mean for me?

I did not write any of the songs, I was solely asked to come up with and play the parts

This may be something you can say to them to ask for a small consideration, on the grounds that you had to spend more time actually writing a part to their song. It most likely does not entitle you to royalties, but it could get you some extra cash.

What should be my next move to secure any royalties that I am owed once it is released?

Get a time machine, go back to when you were asked to write and play parts, and get a contract stating a schedule of royalty payments.

Are they legally allowed to release this music without a contract confirming my consent?

Yep.

If they do come up with a contract, am I in a position to amend it to be in my favour due to their lack of forethought?

Possibly, but I wouldn't be surprised if they amend it in their favor due to your lack of forethought.

Am I in a better position for not having signed a contract or not?

No, but better luck next time.

Pros Cons
You didn't have to negotiate royalties, so no stress from that. You put a lot of effort on the line to get short-changed.
---------------------------------------------------------------------- --------------------------------------
Your name isn't necessarily tied to the project, so if it bombs, your reputation is safe. You have no power to renegotiate the royalty structure or lack thereof.
----------------------------------------------------------------------- -----------
You may get a free copy and a t-shirt. Maybe. You may not get a free copy and t-shirt.
----------------------------------------------------------------------- ---------------------

Moral of the story: If someone wants you to work on a creative project and offers to pay, get it in writing.

/r/WeAreTheMusicMakers Thread