Time for an update.
New tires, rotors, and pads fixed all the bad vibrations.
Four new cats installed, and we fixed about three leaks in the fresh test pipe welds. Still louder than I expected, but in a totally good way.
Compression test completed. Most cylinders are between 205 and 215, with one at 195 and one at 240. We think the high one got a little bit of oil in it, because the spark plug well was nearly full of old oil (from leaks at the back of the cam cover from what we think is one of the VVTi actuators). We squirted a little MMO in another cylinder, and it went from 210 to 270, so we're probably right. But what is the right range of values? I searched and searched online and could only find one reference to 190 psi for a version of this engine with lower compression (static compression ratio for this version is 11.8:1 (!)). I found two videos of two different shops doing compression tests on these, which were apparently engines for sale. Both of those had values similar to ours , 210-230 psi. So I think, tentatively, compression is OK, which implies rings are OK. I don't have a leakdown tester, and since the compression seemed OK, I didn't buy one this weekend.
Since I'm facing potentially $xK to replace parts, I told the boy we're gonna try some snake oil solutions first. First up is Marvel Mystery Oil (MMO) in the spark plug holes. I'm starting there because even though the smoke signals and compression test are telling me valve seals, the Toyota/Lexus shop that my son called insists that it is always rings. According to The Internet, the MMO contains solvents that will wash away crud that keeps the rings from doing their job. The MMO went in on Saturday and we (95% him) buttoned it back up tonight. Plugs were uniformly cruddy but not worn. They got wire wheeled and reinstalled. I was told to expect some smoke after we started it. Tha dense fog that covered the Mid-Atlantic this evening between 6:30 and 7:30 was us. It smoked and smoked and smoked. Finally I had him take it for a ride and 99% of it went away in 10 minutes or so. Sounds fine, runs fine, and drives fine, but it did that before too. At least I haven't made it worse, yet.
Snake oil #2 will be a Rislone product that also has solvents in it, but is, according to The Internet, much better for crankcase use than MMO. The theory here is that the solvents will do what the MMO does, but slower, and also swell the seals. I get that this is long shot, but this stuff is cheap, so we'll give it a try.
Snake oil #3 is another Rislone product that is essentially like the other "rebuild in a can" products that have been around for ever. These products supposedly seal things up for 1000 miles or so. I wasn't interested in this one, but he bought it by accident, so we'll give it a try if the other stuff doesn't work.
I'm hoping for steady improvement in oil consumption. If that doesn't happen, next step is to get a pro mechanic friend of ours to do a real diagnosis. I've noted the comments about the Tech stream, brake bleeding, trans fluid, and PCV. We'll get to that.