I’m going to experiment with the kiln and see what happens.
Certainly do that. I like to have an opening at the top about the size of a cantaloupe or a basketball for each cord enclosed in my kilns, but I am getting 22 hours of direct sun on my kilns up here. I don't know of anyone in any location having bad results with passive solar firewood kilns. For me local I don't like the short life expectancy of my plastic membranes at -40 and -50 dF, the plastic just gets real stiff and cracks super easy in cold weather.
There are many many burners in the PNW running Douglas Fir, seasoning one year (one full summer), and having good results.
Last year, maybe year before last, I started burning (pseudo) hardwood 'birch' in my shoulder seasons. In early fall and late spring (for me local) having a firebox full of coals at +/- 600 dF is enough to keep the chill off the house for 24 hours at a time, give or take. You might be able to do that with your oak as well once it is seasoned. When 24 hours burns with birch aren't keeping up for me anymore as the snow accumulates, I just transition to 12 hour burn cycles with spruce, blah blah as the mercury drops.
I do encourage you to get familiar with DFir if you aren't already. I think of Doug Fir (and Southern Yellow Pine - SYP back east) as the 'tweener' woods between familiar Spruce-Pine-Fir (SPF(s)) softwoods and the various hardwoods. Both DF and SYP can be seasoned fairly quickly, but punch above their seasoning time on the BTU/cord scale. FWIW 'SPF' is a little bit stronger than SPF(s), and grows in Canada. SPF(s) grows in the USA with a lot of overlap among species, but ultimately SPF(s) is a bit weaker in the various engineering values.
Tamarack is pretty good firewood that should season quick if someone offers you some.
The main thing with wood stove fuel is to get your rounds split at least once ASAP, stack them off the ground and get them top covered so the clock can start moving.
FWIW Oregon White Oak, Quercus garryana, is in the Beech family,
https://owic.oregonstate.edu/oregon-white-oak-quercus-garryana . You might pick up your scraps from splitting, put those in a pierced foil envelope and try cooking some potato on your gas grill with just a bit of olive oil and salt. If the potato are good, try some beef or chicken. If the potato suck, take the rest of your scrap to the landfill or use it as kindling. Regular back east American Beech, Fagus grandifolia, subject to a new blight, is a very mild BBQ wood with quite a delicate flavor that works on beef and pork as well as poultry and shellfish. I will probably try smoking cheese on F. grandifolia someday- oh wait I have all the hardware I just need some free time.
FWIW if you come in to some Blue Oak (my mom in northern CA has one in her yard) you should definitely get some of that just for cooking. Blue Oak is fabulous on beef as red hot glowing coals, and pretty darn good as a smoking chunk on charcoal for beef. Blue oak should work good on pork with some hickory or pecan, and should do fine on poultry alone, but all of mine comes home in a checked airline bag, so ribeye and porterhouse at my place.