I've found wiring to be an issue with newer Toyota's. I'd install a jumper to the hot side of the coil while cranking & check spark then. If spark looks better there's a wiring issue that's causing most of the battery power to go to the starter, draining the power source for the coil.

To further test this, install a jumper between the starter solenoid (the start spade on the solenoid) & the battery & test ignition spark again. It should again be strong & bright.

If you find these 2 test bring the cranking spark up, install an external solenoid in-line with the feed wire to the starter solenoid so the new solenoid connects the start spade of the starter solenoid to the positive stud of the battery, with the existing wiring feeding the starter solenoid feeding the new aux solenoid.

And- you are correct that starting on LP requires a stronger spark then starting on gasoline. With that said- you should be able to start on LP no matter the temp- all of the units I service are strictly LP & all are operated year round- most are operated outdoors and are in unheated situations.