Disclaimer: my mindset is gas vs electric, not propane vs electric, since I get gas delivered by PG&E to my house.
So you need to think about this in terms of both energy and power.
The main intersection with NEM3, if you care to use NEM3 vs a non NEM interconnection plan, is that NEM3 sizing is based on how much electricity you use. Not sure how much they'll enforce for the small size of system under discussion here. Also, if you hire out the project you can probably get a better deal doing it in one chunk, instead of adding more later. Permits and interconnection have a fixed amount of red tape per project, so if you do it in one shot vs two, you save the headache.
furnace, tankless water heater, dryer and stove
I would say in terms of impact, go after the water heater first. Then pick between dryer and stove depending on the non-energy benefits they give you, as well as your habits. For instance, we don't run that much laundry through the dryer, and looking at my consumption data I easily use 2x more energy per month on the induction stove than the resistive dryer. But a family that generates a lot of laundry would easily reverse this. Switching from gas to induction gave me a nicer stove to work with, while switching to a better dryer ... maybe vaguely is more gentle on my clothes.
If you're thinking about EV, I would work that out first before the furnace, since you can easily offset non-winter EV use with a reasonable size solar setup.
Furnace would be a real challenge to offset with solar. It is one of the biggest energy and power users. And it needs the energy in the months without much solar. Furnace is the highest energy in the house, and either #1 or #2 if you charge EV at home. I think you can maybe offset the heating in shoulder season, which admittedly is pretty long in the Bay Area. Where I am, March through May, it's feasible to generate enough from rooftop solar to heat your house completely.
Tankless is a massive power user and the second most energy in the house. Tankless water heater can be swapped out for Heat pump water heater, and there are some quite decent local incentives. HPWH use a lot less power, over longer time, which helps with solar. Peninsula Clean Energy is offering $2000 for a swap away from gas (not sure if they cover propane). The main constraint here is whether you can fit one in. They are way bigger than a tankless. They also make more noise than a regular tanked water heater. But they should be much quieter than a running tankless heater.
Stove is high-ish power but does not use very much energy. My home office uses more energy per month than my kitchen. I cook a lot and I'm super happy with induction, though it may be a bit challenging to find an induction stove that responds the way you want. It is pretty easy to find one with way more power output than you can handle, and delivering this power without heating up the house. I actually have to bundle up in the kitchen sometimes.
Dryer is a massive power user. The HP dryer will make drying much easier to run off solar. Dryer often is well behind water heating in home energy use, of course it depends on how you use it. This segment of appliance is innovating quickly, so there are more options than ever. The improvements are mostly around things like form factor and ease of cleaning rather than efficiency.
Another advantage of HP dryer is that it will save you a bit on heating bill, since they are unvented and do not draw heat out of your house during operation.
