not sure if they are compatible so i cant help you there, sorry. i definitely feel like its a problem with transferring over from start to run. it might be possible that the 1.8 isnt powerful enough to efficiently turn over the 2.0, but wait for other input, im just throwing out possibilities
I haven't looked at any specs for the 1.8 version, don't know if the starter is at all different. What I do know is that the 2.0 FS is rather easy to start normally, you can jumpstart it cold from just over walking speed. I have gotten mine running in negative 20 celcius with a bad battery with the starter just bare barely running.
Not sure if there are any differences on the engine harness, but have you changed that to the 2.0? Have you tried starting the engine with the spark plugs out to confirm that they are in fact giving sparks? Checked for error codes?