Really having a hard time understanding why this is so difficult for you? Not trying to be insulting, so please don't take it that way. I worked in a walmart tire shop for 6 months and never had much trouble, even with big 22's and large mud tires on trucks. I did have trouble with the foreign car that had wheel studs instead of lug nuts but, that's a totally different issue.
The only possible problem I can come up with, is that you don't have the vehicle jacked up high enough. If it's not jacked up high enough the tire will hit the ground when tilted before making contact with the studs/hub. You should be able to pick the tire up, let the top tilt in (bottom out) and slide the wheel on the top stud. With the wheel hanging on the top stud you should be able to align the wheel to the other studs by turning the wheel. It might be helpful to put on the parking brake to keep the hub from turning.
If you are confident that the vehicle is supported well and isn't going to fall on you, you can use your legs to lift the tire instead of your arms. Essentially your legs would be like the rollers on the dollies shown above and you can use your legs to lift by bending at the knees while sitting on your butt.
I love, love, love your Vette btw. I live just outside of Bowling Green, KY where they are made and I get the pleasure of seeing them on a daily basis. I still have a mountain of student loan debt to pay off for now but, I will own one some day.