Long-time intermittent rattle/shaking suddenly became nonstop

Hey everybody, 2010 Prius, 201,000 miles, engine suddenly shaking/rattling like crazy. The first and most important detail of this problem is this: It's done this exact thing intermittently ever since we bought the car 100,000 miles ago.

Before, what it would do, is every once in a while (every couple months) we'd move the car in the driveway a few too many times without it fully warming up, and then on one of those startups it'd shake/rattle like crazy. Shut it off, restart, it might do it again for a few seconds but then clear out and run like it's fine.

Again, this car has done this, intermittently, once every couple months, a few seconds at a time then fine, for 100,000 miles.

A week ago it suddenly did it in a totally different situation with my wife at the wheel driving home from work, fully warmed up for 20 minutes, suddenly starts doing the same rattle/shake. She pulls over and calls me. I can't get it to go away.

Over that 100,000 miles, 7 years of ownership, the coolant has very slowly dropped in the reservoir from max to near low.

I don't think it's the head gasket. I've been a car guy my whole life, fixed all my own old cars for 30+ years including head gaskets, grenaded modified engines and total rebuilds.

Why not? Because I put it in neutral and the sound and vibration goes away completely, instantly. It now does this hot or cold, all the time, but only does it in these conditions: when it's in park, when it's in forward or reverse, and it's anywhere between idle and half throttle. AKA any time it's charging.

If I put it in neutral it goes away completely. If I drive it above half throttle it goes away completely.

It's giving me a code for a "random misfire"

At this point I'm thinking it's EGR or a horrible transmission/clutch spring thing.

I've cleaned the EGR system, intake included, twice in this car's life, once at 125,000 miles, then again about 5,000 miles ago. That's throughly blowing out and chemically cleaning out all the passages, the valve itself, the cooler, all that. I tried the EGR valve-to-intake-pipe blockoff trick thing and it didn't change whatsoever. No idea if that truly rules out an EGR system.

I pulled the ~2"x3" black plastic cover off the underside clutch part of the transmission facing the engine and felt around in there and I can't feel any detritus or broken springs. But there wasn't much room to feel around down there.

Did the plugs 15,000 miles ago with OEM factory replacements btw.

Ideas? Thanks