Not totally sure about this, but I know there can be issues with the flywheel sensors. My brother had an issue with starting on his 944 and replaced one and it got it going. He replaced the sensor closest to the drivers side and the car started, so even if it is to spec, for $30 bucks it might be worth a try.
There is a way to do a temporary jumper wire on the fuse box from 34 (fuel pump) and another 30amp from near by, then push the fuses back in, that takes care of the non-running fuel pump. My brother has to do this on his 85 1/2 944.

One more idea. My brother had an 83 944 with fuel pump not running. It sat for a while and I finally took a good look at it. I had been working on a 74 Porsche 914 at that time and had a few cases where electrical connections were corroded but also had a case where pushing in a relay actually backed out the connector on the other side. So when I looked at his DME relay I saw that one of the wires on the backside of the connector was pushed out therefore when the dme was pushed into it the wires never made contact. So I reached back there and pushed the connector into the right place plugged the dme into the socket and viola, the car started right up. He was like “Dude you’re a genius!” (That’s how we remember it anyway doesn’t happen often). Good luck.

I hope with the time you have you can get it going again. As far as the injectors if it runs on starter fluid it makes sense that the injectors are not the problem. Keep in mind there are four of them. From what I’ve seen injectors make the difference between running well and not running well but not a non running issue.
Have you looked at the in tank filter? If it’s a steel tank should be easy to remove if it’s a plastic tank be careful it can be another issue if the aluminum sleeve starts slipping when you are trying to remove the filter. I had this problem and found a purolator filter with shreds of filter fabric everywhere. Perfect material for clogging the fuel pump and filter. I ended up buying the $160 fuel tank boss to stop the tank leak issue. Epoxy is not a good solution.
Good luck on getting it going.

Cars that start but run poorly at least have a starting point and you can go from there . When it’s a non running condition it requires a lot of trouble shooting and it could be anything or it could be multiple problems at once so like you found out fix one thing and fix something else and then it runs. On my 914 I took the injectors out put them in a jar and turned the key to start to make the fuel pump run but not the starter. I found I had an injector not producing any gas. I found out it was the electrical connection. I cleaned it up and got it going. My thought is if it runs on starter fluid it’s not the injectors. Fuel line hoses on these old cars are often corroded. I got a non running 944 and tracked it down the the in tank filter and the fabric got lose and was being sucked into the fuel pump and clogged the system. I drained the gas pulled it out and found the remains. The brand was Purolator so I thibk that’s not original Porsche equipment and may work fine for a while but deteriorates. My logic is start at the begining and go from there the fuel injectors are the last link in the chain. First gas then tank filter pump and filter. I cut one of my lines horizontal after I replaced it to see what it looked like inside. It was a crusty mess and cracked. Almost split by hand no I’m in process of changing all the fuel lines front to back a very expensive process. I also have a replacement boss in order because the fuel tank sleeve stripped and the seems the best solution. (I have the plastic tank) in the end by process of elimination problems are always resolved cars are always subject to science and logic.

I can’t help but wonder did you get this car going yet?

bad smell seems like bad gas ? I just got my 944 fuel system together last night just need to add some gas and start it. Should be good to go. Had to replace 7 items from tank to hard line all brand new including aluminum tank boss to fix a stripped collar. So this was a costly repair and took some time to get it all on there but it’s done now. I hope you can find the fix and get it going.

I have a compression tester coming in the mail not here yet. Will do those tests when it comes in. Smoke did not smell of sweet radiator fluid and exhaust pipe let out smoke for about 30 minutes after car shut off which I thought looked like oil burning somewhere.
Also looking into security system module causing problems.