I think I've flown into and/or out of LAX at least once/month since this whole thing started. I live in LA County about an hour from LAX.

If you want to try to get a hotel room, call directly and ask what the actual restrictions they're operating under are - I think "essential travel" may be interpreted more broadly than some of the short announcements indicate, and guidance for things seems to change almost daily as issues arise and get clarified by health officials. If you've been in CA for some extended period and are returning to Canada, it may be acceptable, and they may be happy to have you leave the state. If it's only a few hours, i'd consider parking somewhere and napping in the car. If for some reason you end up going airside at night and killing time there til morning, probably the least contact with people is in the skyway between T6 and T7.

As far as getting through the airport: I'm always flying domestic so I tend to plan to get to the curb 20-30 minutes before boarding. You might want to aim for a little earlier if you don't have pre-check or CLEAR, but lines at T6 have been fairly quick since the pandemic started, so bag check cutoff will probably drive your schedule. Depending on the length of trip, I either take a Lyft (long trip) or park at QuikPark just outside the airport and walk to T6. So if you can just start later from wherever you are and plan to arrive at the airport in the morning, rather than the night before, it might be the least hassle.

Almost all the food in T6 is closed - I think The Habit was open last time I went through, but that was it. The newsstands are open. Alaska Lounge is open again, as already mentioned, and I think you can sit inside masked and not eat (better isolation than the terminal) or get food to eat out in the terminal. As mentioned, they take priority pass, and if you've got the Alaska credit card it's only $25 for a day pass.