Most areas will NOT allow any gas piping under a slab, period. Using an electric boiler for radiant heating could make you a millionaire, assuming you start as a multi-millionaire.
In parts of the PNW it's cheaper to heat with an electric boiler than it is for me to heat with natural gas. The natural gas comparison may or may not be the case in Chelan, but the cost of heating with propane is often more expensive than heating with electricity in that region.
But even with 5 cent electricity or whatever I'd be inclined to do the heavy lifting of the space heating with a high efficiency ductless or ducted heat pump, even if keeping the slab warm-ish with an electric boiler operated off a floor thermostat. Chelan definitely has a cooling season, and the up-charge for heat pumps rather than split AC isn't too huge.
No matter how you're heating or cooling the place, run a formal Manual-J heat load calculation for sizing it correctly. With electric boilers that doesn't matter as much as with fossil-fired boilers, but sizing the AC correctly delivers the highest comfort & efficiency at the lowest up-front cost. With the typical negative latent loads in Chelan don't be afraid to go with very high SEER modulating mini-splits for cooling. You don't need much if any latent cooling, and even a 30+ SEER ductless won't leave you clammy or sticky, whereas a 13 SEER split system can even over-dry the indoor air in summer.
Reversible air source chillers for heating the slab are also possible, and can also provide decent cooling in that climate without much risk of condensation or mold on the flooring.