Try lug nuts that go deeper....they are available (shoulder is longer than normal). You have more tread to grab with. Just bought a set at Advance Auto, did not work for me, so am returning it. The shoulder was too deep, it was bottoming out. Trying to install a Lexus 5 spoke GS300 rim to a 98 Camry. Good luck with yours. Pics good, post them!
If you're trying to use the lugnuts for steel rims to hold alloy rims, they are very different. The alloy lugnuts have a threaded part that fits into the hole in the rim about 3/4", and a washer that sits in the recess of the rim around the stud. The steel rim nuts have a simple cone shape that goes into the steel rim hole, and will not work with alloys.
If this isn't your problem, have fun pressing out 20 studs and pressing in longer ones...but I can't see this being correct unless the new rims you have weren't meant for your car in the first place.