Rebuild time is approaching and there's a DIY auto place near me that has lifts.
With a lift and appropriate transmission jack I think it should be simple to lower the engine and transmission from the bottom of the car.
Basically like doing it from above except the steering gear under the oil pan has to be unbolted but the hood and radiator can be left in place.
I think there should be room for the engine to move back a bit so the cross member can stay in place.

Anything I'm missing? The shop rents the bays by the hour so I'd like to minimize time.

 

I would first ask why you want to remove both. No need to remove the transmission when rebuilding or replacing the engine. In my experience, I find that the engine comes out easily from the top and all bellhousing bolts are very accessible, top and bottom. I feel that its much easier to remove the radiator and supports versus trying to slide the engine back and down through the trans tunnel. Dropping the engine and transmission together would be fine, but you would want to remove the engine mount crossmember straight down with the engine bolted to it and the trans bolted to the engine. But before doing that, you will have to remove the exhaust center section, driveshaft, and heat shields. All of that is much more work than simply removing the engine from the top. If you do decide to drop the engine and trans straight down, I would lovento hear about your experience with that method. Maybe you're on to something.

 

I have a rebuilt transmission ready to go with the new engine so the old one is coming out regardless.

 

Yes, when I did it at a friend's place who didn't have an engine hoist. Or a garage. One of those start pulling on Friday after work, rebuild engine on Saturday, reassemble Sunday so I could drove to work on Monday kind of deals.

It was really easy because I had an FC subframe. Four ball joint bolts, two tie rod nuts, one steering shaft bolt, two motor mount nuts, and four subframe bolts and everything was out of the way. Supported the engine with a ratchet strap and dropped it down to drag out from under the car.
Shoving it all back under the car on Sunday, when it was like 95 and no clouds, however, sucked.

I wouldn't bother with the stock suspension, as it is much more fiddly to drop out of the way. You probably won't be able to sneak it through without removing the crossmember.

I have removed the engine without removing the hood, and I have even done it with a (Respeed?) 4 point strut tower brace in place. That said the RX-7 hood is the easiest thing in the world to remove and install one-manned, undo the left side bolts, undo the right side bolts, and it will still sort of be supported by the front panel and the prop rod. Then you just lift it off.

Transmission jacks are sketchy, wobbly nightmares and I never use them if I can avoid it. When I do a transverse transmission I work with the car only a couple feet off the ground and I use an engine hoist to lift it up into place. When I replace an RX-7 transmission, I put the car on a lift, and just pull it out and throw the new one in by hand