Okay, re the packing, you're referring to part 16 in various thicknesses. I'm not sure why there is packing only on the back side but I'm guessing the factory used it to offset the weight of the head stock that projects behind the ways. Regardless, you should still be able to level the lathe adequately with the bolts under the head stock and I don't think that shim will influence that. Well, it doesn't influence my lathe anyway.
Please pardon me, quickcut, but I'm totally confused about the MT5 taper thing. You're saying you have a 35mm spindle bore with a MT5 taper. This implies you have a D1-4 spindle mount, yes? The MT5 does require "short" MT5 tooling; a normal length MT5 taper will not go in all the way. My MT5 dead center has a total length of 2.05"/52mm from the small end to the large end where it goes into the 60 degree taper. The small end measures 1.668"/42.37mm, and the large end measures 1.753/44.5mm.
So, your 5c collet chuck has an MT5 taper on the back but it won't go all the way in, right? But here you say that the chuck is much shorter???
I have the collet chuck, the taper is correct ,but the chuck is much shorter than a standard length MT5 . The bore of 35mm does not allow a MT 5 whose" thin" end is approx 37mm.
It sounds to me like the MT5 taper on your chuck is too long, or at least too long for the existing taper. Again, note that the proper dead center for this lathe is only a bit over 2" long and if your MT5 taper is longer than that then it won't fit.
Anyway, why not just get the precision rod and indicate it in the 4 jaw chuck? If you indicate near the chuck and another point farther down the rod then it will be accurate enough to assess the head stock alignment with. Or you can just chuck up a 6" length of mild steel and take skim cuts about 0.002" deep and check the OD at both ends and in the center; that will tell you how well the head stock is aligned with the ways. If you are more concerned with leveling then a 2 collar test with a longer rod is probably more helpful.
Personally, I would trust a 4 jaw chuck that I indicated the rod to zero in before I would trust any collet, 5c or otherwise.