All good edgie, glad I could help out. Yes, my/the '62 custom is what Nolly's '59 is describing, there looks to be a fine tuning of the name as Tim gets closer to an official release of pickups. The custom '62 was at one time called the # 1's, I forget who here had the first set of these and that was a temporary name too.
You gotta love how BKP puts in years of R&D before finally releasing a product, and willing to wind & sell along the way of development, this company has product and Cahoona's! Sometimes I have to look at my pickup selector switch to see if I'm on my humbucker or my single coil, because the single coils can be that quiet at times! I don't use a full pickguard shield anymore, just the control section of the pickguard is shielded.
Ya Nolly's up on things better than I am at this time, and I might add you can count on Nolly's words being strong, my opinions concur with his the more I buy and experience BKP as related to Strats with solid alder bodies.
I listened to your link of Jimi's recording, depending on the sum of your whole signal chain, I think that tone could be gotten with a custom '62/'59, '63, or '69, yes there's a '69 in the wood pile too! You can't go wrong really, it's hard to hit the nail on the head 1st time around, however (i.e.) I'd trade my '62 for a '69 right before I walked onstage and not be worried a bit. I say pick the one you're feeling at this point and jump on in! :)
WR