After poking around and seeing what's out there, I've decided to go with the ATtiny3224. This will give me far more space to put in text and graphics, while also supporting the simplified single-pin programming interface. The 14 pin SOIC package is still easy enough to hand solder, though I might end up doing these on hotplate anyway.

Since I'll have the extra pins now, I might as well hook each of the LEDs up to one of them for independent PWM control. Don't know that I want to do flashing or fading, but I could at least support multiple brightness levels.

Also planning on breaking the programming pin out to the SOA header, so I don't have to come up with some kind of alternate interface to flash them. The plan is to use the 4-pin SAO header on the Supercon 2023 badge, so there's no chance of a conflict there, but I'm thinking it might be prudent to add a solder bridge flash enable just so the programming pin can be disconnected should it interfere with 6-pin SAO badges.