Thanks to everyone for the info! I'm sure that this will help more people than just me!
I think I'll just get a new one that's meant to be a headlamp, as opposed to what my 2014 MagicShine was: a bike light strapped to a headband. Seems like I can get something just as bright as before, that's more comfortable on the head, doesn't require snaking a cable to a larger battery, and has the flexibility of just getting some extra 18650 batteries if I need them (for easy replacements, or if I'm doing a 24h event).
I saw the Fenix brand at REI before Alex posted, so that seems reputable.
The HM65R-T is the Fenix one that caught my eye. I want to get something at least quasi-reputable, I don't want to play eBay roulette with a bunch of $15 options, haha. But I also don't want to overpay for less-bright "big outdoor brand" lights, either.
One thing I like about both the Fenix light I linked, and Sharon's recommendation, is the two light system: one for distance, one for flood.
I went down the rabbit hole through Mark's reddit link, and I discovered the
HS-20 from Sofirn, which ticks a lot of the boxes I'm looking for: throw and flood dual LED's (2100 max lumens), an easy and flexible battery situation, USB-C charging, waterproof, from a quasi-reputable brand, and is pretty inexpensive (just $33, after 15% coupon code, and shipped from California).
I say quasi-reputable because Sofirn products are all over that flashlight aficionado reddit thread, plus I found some very detailed reviews about the HS-20 (including
one specifically from a trail runner and a few on YouTube). But it's still a brand that I hadn't heard of before.
And if you are still reading this and you're interested in the HS-20, here's something I found that you may find useful. There are two versions: an older one with an XHP50.2 LED for the throw that claims 2300 max lumens, and a newer one with an SFT40 LED for the throw that claims 1600 max lumens (both versions have the same LED for the flood). The SFT40 actually has a further throw, despite having fewer lumens. I saw several photos and YouTube reviews showing this. Anyway, if you have a preference for throwy vs floody (or vice versa), now you know.