Yes I had my belt on, there's nothing more distracting than when your trousers fall down in the middle of a tune.
I think the tips on learning from session players on this thread are really valuable. I'm outside of the folk sessions world and I am always amazed at their powers of memory. I thik there's a lot in this thread on how the brain learns.
The thing about names of tunes is interesting because I know a couple of veterans of the hotel bar circuit who played standards on their accordions (often with simpler chords than would be on the sheet music, that's an observation not a criticism) and they tend to sit down to play with a list of tune titles. That's all, no notes, no chords, just the titles. But both said they would lose their way without the titles to trigger their memory.
On the other hand, my sister's a pro musician (West End shows, freelance orchestra and opera work, some pop recording) and you don't get that work unless you know what you're doing. Her sight reading skills are terrifying (and I'm talking about expressive playing, not just mechanically reproducing notes) and at any one time she has some complex classical pieces up her sleeve that she can play by heart. But how many songs/tunes/pieces does she know by heart at any one time? I don't think she has ever thought of even answering that question, it's not what she does. Totally different skills, totally different learning.
I'd like to be able to do all of it, but it's not going to happen.
David, to come back to your question, because of how you're learning, by ear, by memory, I suspect the answer will be that you can remember a lot of your tunes at any one time. I have found it helpful as memory training to play through all the simple tunes that I've learnt by ear (not the partly improvised stuff, the tunes that I learnt in a fixed form) in a medley, then have another go at the ones that gave me trouble. This seems to help me or give me confidence in my memory.
(Sitting with a sick person today so I might be rambling on a bit, time on my hands.)