Transmission and compression questions.
 

Long story short, shop screwed me with the install of a rebuilt engine into an old used car, and now the engine and transmission kick like mad even at idle. From inside the car you can watch the shifter rapidly jump an inch or two, whether in neutral or in gear, clutch in or out. Problem gets worse at higher rpms. Current plan is to pull the transmission and check how it all mated up, but I'm not even sure what would cause this vibration. Has anyone seen this kind of issue before?

Before I really get into this though, I'd like to make sure the time spent working on this isn't wasted, and I obviously don't trust anything coming out of that shop anymore. So, I ran a compression check that came back at around 60 psi at 150 rpm (weak battery), which isn't great, but seems survivable after adjustment if I ignored two important points. First, it's a fresh engine, and from what I've read these engines build compression during break in. Second, because I'm worried about damage from running the engine, I tested cold. How much of an effect will these two things have on the compression check? In your opinion, is the engine still worth trying to save, or should I spend this time installing a new engine instead of trying to fix whatever is going on with the last installation? Thanks everyone.

Cold test shows higher compression than actual, and 60 psi is super failing even at 150rpm. I wouldn't make decisions based on these results. Does it start? What kind of tool was it tested with?

As far as the transmission problem, how does it jump exactly? If the engine mounts are busted it'll certainly move some, and that is a common issue on RX8s. Does it jump left right or up down or forward back or alll of the above? Mounts are easy to replace. If they screwed up something like the power plant frame alignment, that's just negligent and more of a pain to redo.

That said if a shop gave you the car with issues, I'd get them to own their work. You didn't pay them to create new hobbies for you.

Starts alright, about what I'd figure from a weak battery and a fresh engine. The motor mounts are fine, I replaced them the last time I did the engine and while they're solid, it's never shaken like this even up at red line. Not even when they were completely torn, back when I first bought the car.
Most of the vibration seems vertical to me, though I've mostly been in the car when it's running and it's hard to ignore that shifter jumping. I wouldn't be surprised if there was horizontal movement to go along with it, but I don't think there's much movement fore and aft. Makes some sound around the front of the cabin, probably far enough back it's the transmission and not the engine.
Compression numbers were on a simple pressure transducer connected to an arduino, and I haven't calibrated it for a while. They're probably inaccurate, but I mostly use it to check for consistency across faces and rotors rather than overall health. If I do make it accurate, I'll still need some more info. I'm curious the differences in cold and hot pressures- 10%? 20 psi? Same story for the fresh engines vs. the broken in ones- do engines pick up 5 or 15 psi? I should have stated the question a little more clearly before, sorry about that.

If I could deal with the shop, I would. They're arguing the parts are at fault (they did do some work on the oil pump). And they "never saw it run in the first place", so they don't believe that it was running well before. Short of a suit I can't afford and burning quite a few connections and relationships, I'm not getting a penny or an hour from the shop.

Supposedly freshly rebuilt engines will build up compression over time. I'd give it one or two thousand miles. What's the shop's warranty on the rebuilt engine, if any?

It sounds like they forgot the power plant frame entirely. Otherwise it's not super possible for any of it to jump up and down. Can you check that there is in fact a giant rail running parallel to the driveshaft and connected to the diff and trans?

All kinds of bad things happen to the trans and diff bearings if the PPF is not in place.

With everything, I'm sure there's no warranty any longer.
PPF is there and on tight, at least on the transmission side. Which is part of the worry- I've never seen any powertrain do things like this without major problems. Though admittedly my experience is limited. I would give even odds they pulled the engine from the hood and didn't touch the transmission...and that the problem is in how the two meet up, though I'm less sure of that. Just my brainstorming here, could there be problems with the surfaces of the clutch/flywheel? Lost/doubled/smashed bearings causing parts to grab that shouldn't? Bent input/eccentric shafts from dropping the engine hard before they were properly aligned? Counterweight in the front plate stuck on upside down and backwards? Wiring precoil causing the engine to fire backwards?

But it's looking like I'll just need to pull it all off and look, isn't it? Which brings us back to compression numbers. If I'm pulling the transmission, it's probably a good time to pull the engine too, if it needs replacing. Thanks, by the way. I really do appreciate the help.

Is it possible only the shifter is jumping or the actual trans? The shifter could just be poorly secured I guess.
With the PPF in and connected the rest of the powertrain can't really move up and down. Check the motor mounts?

The PPF connects the engine/transmission to the diff and makes them a single assembly. The whole assembly is basically suspended from the engine mounts up front and the diff mounts in the rear.

If the PPF is there, secure, and aligned correctly then the only way for the gearbox to move is for one or more mounts to be bad or not connected.