As others have said: You'll spend possibly _days_ trying to cool the setup with the engine in a vacuum and and a gap packed with dry ice.
Just drop the dry ice into the hypobaric chamber, cool the whole mass and then draw down the vacuum. You'll only need a couple of minutes of vacuum pump operation to achieve < 1% pressure (it's the last few millibars which are the hard part and even the best setups on the planet can't achieve/maintain the fractional pressures found at only 150 miles up.)
Granted you'll only keep the low temps for a few minutes but that's all you actually need. Embrittlement of gaskets, etc isn't something you need to worry about for this kind of duration.
Perspex lid: Good, but 8mm laminated glass will work just as well, be far stronger than anything you need and be reusable (your local glass merchant will probably have anything up to 50mm glass circles on hand. Anything larger will need to be cut to order). Personally I'd put a wire cage over the top to stop it flying, rather than relying on a retaining ring and chain (which could have the lid flying on a wild arc if pressures are high)
Mirror for camera protection: Good
Given the size of the motor, You could forgo the whole chamber manufacturing process and just put the whole setup in a chemistry lab gas jar. They're strong enough to withstand a couple of atmospheres of pressure both ways and have flanges (test it empty, of course.)
With suitably thick gasket(s) you can run the sensor wires and vacuum pipe between 'em (sandwich style) and not have to drill any holes.
Anon because I work in a space lab. Our hypobaric chambers are "somewhat larger" than the one envisaged and get "somewhat colder/hotter". A full space component validation takes several months....
WRT the comment about hauling liquid nitrogen around in thermos bottles: That's fine as long as there's a hole drilled in the lid. I've seen the results when someone didn't do that. (A 0.5 litre thermos bottle holds quite a bit of pressure and the results of failure would likely be fatal to anyone within 5 metres.) Bear in mind that it's illegal in the UK (possibly EU wide) to transport LN2 in this manner because of the risks of something like that happening (if you're going to insist on putting LN2 in a thermos, DON'T put a lid on it - even with a hole, there have been instances of that icing up!)
FWIW we pay about 10p/litre for LN2 but we do buy 4 tonnes at a time. 100 litres is about 12p/litre and the companies will rent you a suitable (large) dewar to hold it, but you need cryogenic handling training before they'll consider it.