Then we have an intermediate shaft issue.
The motor, with that trans, should have no issues with the correct intermediate shaft and axle setup.
Pic of AWD DSM turbo axle setup 05.1988-05.1994
Click for DSM AWD Turbo intermediate shaft picture
Pic of FWD Mirage/Colt turbo intermediate shaft 04.1988-04.1992
Click for Mirage/Colt FWD Turbo intermediate shaft picture
For future reference, here is the listing for the spacer to fit where the AC bracket would normally reside. This is the AC delete spacer.
32183 MB297732 SPACER, FR AXLE. Period: 1988.04.1-1989.05.3; Part Spec: 13; Size: 13 02
Spacer:
Click for JNZTuning part
I have used the following combinations, all with the stock C53A intermediate shaft and axles, original motor and trans for a C53a and now the 4g63t and related FWD trans, all with no binding or fitment issues.
4g61t - KM210 FWD 5 speed
4g63t - KM210 FWD 5 speed
4g63t - F5M33 FWD 5 speed
For reference, my 4g63t motor was imported (red top) as a JDM motor/trans (4wd switchable) combo.
It was installed into a 1991 Eagle Talon AWD. 4g63t block with AWD trans.
Have to install the correct intermediate shaft hanger/related parts to match the transmission combination, the bolt holes on the blocks are all in usually in the same place.
Heck, they made 4g15's with 4wd .... but lets not go there because that is another can of worms entirely on its own.
Mirage Performance thread showing DSM AWD intermediate shaft from Raxles.com
http://www.mirage-performance.com/sonata/Axles/
These are the best pics I could get, at night, with my phone pressed up against the chassis:
Click
Click
Click
Click
Striking similarity between the pictures of my intermediate shaft and the one you had pictured.
You will notice that on the inboard side, the top bolt hole should be almost inline with the inner most portion of the carrier bearing.
The axle you have posted, shows the inner most lower portion more to the outboard side.
You have the wrong carrier, but if you can get one from a turbo mirage setup, you are laughing because the shaft itself should be identical.
I just had a read over the axle thread stickied at the top of the 4g61/4g63 Tech Section, just to freshen up on this stuff.