I've come up with a new board based on eight of PVT212 and a TPIC6C595 shift register.
Here's a couple pics and a couple of videos of one of the chips controlling a C6060 LED module from 5V, the power supply that came with the module is rated for 700mA, so it's pretty bright.
The chip is rated for +/- 150V (Yes, AC or DC) and 825mA. 0.25 ohm turn on resistance the way I have it wired up. https://www.infineon.com/dgdl/pvt212.pdf?fileId=5546d462533600a4015356841646295d Indicator LED on each one to tell you when it's on if you're using something not quite so obvious (or for development).
Notice how quiet it is - no relay switching noise!