Data, Data, Data. x2 on the Blackstone labs, and I'd look at checking your coolant for combustion gases. It sounds like you're on it.
I would also suggest picking up a
ScanGauge II, and or
UltraGauge for even more telemetry on your engine health (If you don't already have one).
I suspect it may just be a HG issue. You might have a small leak somewhere that's pulling your coolant. That's on-brand for the 1FZ at your given milage. See if you got gas in your coolant.
The oil consumption may be something similar/different.
Background:
I spent about 2 years 'limping' a 1FZ-FE around the country. It had 293k miles and burnt a quart of oil every 800-1000 miles. It probably started ~260k miles, but didn't really manifest until the cats clogged up. I didn't notice any coolant consumption away from nominal. I did experience overheating, and would back off when water temps came up on ~212 degrees. Compression test was within limits. I never did a leak down test.
I had considered everything from rebuilding the engine to swapping a 1HZ into it. The fix was simpler (and cheaper) than that.
Symptoms/Causes:
My primary cause for the oil consumption was the valve stem guide/seals in the head. Oil follows the channels to the cams, leaks down the valve stems, gets burnt during combustion. It was a lot of oil being burnt... Like a lot a lot. Enough to think it was an issue with the pistons/ring/low-end. The new fuel/air/oil mixture burnt my cats up pretty good, probably burnt a hole in my Y-pipe, and created a thermal mass that wasn't being exhausted as it should.
Oil consumption was significantly worse when I was moving slow, i.e. 4Lo. If there was significant highway driving, the pressure from combustion would keep the oil where it was supposed to be, and I would see a 'reduction' in oil consumption, though it was still significant. (See 800-100 miles above.)
I experienced some overheating problems, and went through the cooling system to replace the thermostat, the waterpump/radiator fan. This narrowly improved my issues. I saw maybe a 5 degree drop in my water temps, and would still limp up Eisenhower at 35 mph, creeping up on high temps. I couldn't escape the thermal mass being created by the fuel/air/oil mixture. Even with the cats 'modified,' (Allegedly, your honor,) it ran pretty rough, and would get hot with extended uphill climbs.
The fix:
I picked up a spare head, had it rebuilt at Gunn (for ~$800) and had the old one swapped out. It gave me a chance to look at the cylinder walls. They still had cross hatching at 293k miles. There was no indication that the rings were going/gone. It's a stout engine block given normal conditions.
Since the head rebuild, I go through a quart every 2500-3000 miles. Negligable, as that's my service interval. My running temps have dropped from 195 to 172 degrees, and I have access to power that I never believed a 1FZ was capable of.
If you're leaning into a head rebuild, I've got the one I pulled from mine. It'd be a good donor. Gunn does phenomenal work.
Let me know if you've got questions, or need me to elaborate. I've been kickin' this can down the road for a bit.