Imagine if you were doing this with the body still on.
A few things to make the job easier.
1. Make sure that the trans input shaft fits through the pilot bushing.
2. Make certain you have the correct clutch and spline count, and that the clutch disc is installed with the correct side facing out. They are usually marked to allow you to verify.
3. Use an old transmission input shaft or plastic alignment tool to initially center the clutch disc. Old transmission shaft is better.
4. Put a small dab
of white grease on the transmision input shaft splines (very light film coat on the forward edge of the transmision input shaft splines)
5. Make or buy at least two (2) transmission alignment dowel studs (bolts with heads cut off and about 4 inches in length) that thread into the transmission bolt holes in the bellhousing to help support and align the transmission during installation. You can use 3 or 4 for better results.
6. If needed, have someone push in the clutch pedal to open up the pressure plate and free up the clutch disc to help everything align better during the last 1-2 inches of trans installation.
It sounds like you have done steps 1-3, but no certain about the others. If not, try them. They have always worked for me.