Many thanks to all who've replied.
It looks completely unanimous (is this a first on TML?!) that I should get players to care for their character sheets more assiduously - even if I store them between sessions.
I like the idea of cards and have toyed with it (in fact, for a particular bit of my Ashfall adventure I had a set printed up for the scientists to organize in their base and when disaster struck, had to physically grab what they wanted in limited time), but I think generally - for games every other month in the pub - it would probably be a bit hard to manage.
I love Greg's story of the god not recognizing acolyte because they didn't have the 'thing'! Brillaint.
and the Blades in the Dark suggestion from Phil sounds intriguing. Not sure I could see how you knew what gear took what space in the 'load' though. It's not on the page and I looked at the SRD and couldn't see it there either.
To be fair, I don't think any of my players have been trying to abuse my relaxed attitude to it, and of course I didn't want to inflict too much bookkeeping on complete newbies two years back, but now they're a bit more experienced and beginning to have a better idea of the implications of having, or not having stuff, I think the time has come to be more rigid.
And yes, nailing down the ship's locker for the March Harrier might be a good idea too!