….is it possible? Advisable? I have a decent engine hoist with leveling bar.

 

dont bother. its annoying and difficult as its a bazillion tiny adjustments and a lot of laying down and standing back up. engine first, trans second. the trans is not heavy and can be installed easily if put on your chest. you can use a jack to support the bell housing if you want but its more likely to get in your way. just make sure the engine is leaned back as far as it can be before stabbing it with the trans. it slips right in,

 

I've removed and replaced the engine in my RX7 once, I'm just a DIYer but at the time I had access to a nice shop area including a 2-post lift. I followed the advice posted by Kevin Landers / RotaryResurrection.com , which said to do the engine and transmission as a single unit. It worked OK but the car needed to be pretty high to avoid the transmission hitting on the ground. If you were using jack stands they might need to lift the car as high as possible to have enough clearance. My unsolicited advice is to bag and label fasteners as you remove them because there will be quite a few of them. Attach the labeled bag to the major part they belong with, to avoid a pile of bags that needs sorting. Keep a notepad and pencil nearby so you can write down any parts that break and need to be replaced without leaving the work area and needing to get cleaned up. And have a plan to handle all the fluids that will spill when you disconnect the radiator, oil cooler(s), and power steering lines. It should be possible to unbolt the AC compressor and leave it in the engine bay, if you're careful.

 

If you remove the shift lever you stand a chance of installing everything at once without damaging anything. Get the car high in the air to get enough angle for the motor and trans to go in. I think I had the rear higher than the front. Like mentioned above the transmission is light but lining it up from underneath is a chore, definitely easier to install motor and trans as a unit.

 

I'm with @FDAUTO on this one. Unless you have a lift, and can drop the whole subframe/engine/trans as a whole, I just don't think the juice is worth the squeeze. The throw-out bearing is certainly a pain in the *** the first time you do it, but once you figure out how to do it, it's one of those things that you never really have trouble with again. Just use the widest flathead you can find. I use a crowbar that has probably a 3/4" (or more) wide flat end on the one side. Generally I can get it to pop off with the first twist.

 

I haven't done it on the FD yet but I remove them together on the Miata and RX8. Comes out easily enough. Especially if you have a load leveler on the engine hoist. Also, I find it a lot easier to mate the transmission and engine outside the car then trying to do it in the car. Drain the engine and transmission oil before pulling. The harbor freight 2 ton engine hoist with the longer boom / arm works better than the shorter 1 ton due to how far back these engines sit.

As you can tell from above, everyone has a preference....

 

It can be done with the transmission attached. I've done it plenty of times, just takes a little bit of finesse. Depending on your engine hoist, you may need to add some weight because you are going to want it on the longer arm since the drivetrain sits so far back in the engine bay. I have had some smaller hoists start to lift so having a buddy man the hoist while you direct them and have them stand on the end when needed is not a bad idea if you have one of these smaller hoists so you don't damage your car when it lifts and drops when you don't expect it to.

Like what was said above, make sure the transmission is dry because you need to angle the transmission down to angle it in correctly. Bungee the accessories (power steering, AC compressor) out of the way so you don't have to fight those as much. Air Pump and downpipe can be on the engine as well, though it is easier to do without the downpipe attached. This is how I used to do pretty much all my swaps.

It is really preference @FDAUTO is correct as well, sometimes it is just easier to drop the engine in, then stab the transmission after the fact if you have the car lifted high enough. If you aren't well versed in swapping engines, you can miss something hanging up not letting you drop the motor in with the transmission attached and you may spend hours ftustrated shaking and lifting and moving etc. Where you would have saved that time just doing it in two steps. Figure out what your skill level and confidence is in doing this type of work and go from there. I've known people to not understand that the transmission is hitting something or the intake is hitting a heater pipe and that is why the motor won't go back 1/2" and you may just need to put pressure or lift a specific little section to angle it just right.