It's a hard question to answer. Hopefully, this will help.
If you have the unvulcanized rubber and a rheometer, you can run a sample to the temperature and time conditions you need. The drop from the maximum to the last value is called reversion(or devulcanization). If you are going to extreme conditions, this could get messy.
The standard crosslink density test is the swell test. You put a small amount of sample in a test tube with a suitable solvent (cyclohexane is often used, but many are possible). You measure the original weight and the swollen weight. There are problems. For this to work, your swell time has to be long- say 24 hours. And the dimensions of the part ( both thickness and size) must be the same.
The best crosslink density test we found was swollen state NMR. This is not solid state nmr. It uses a normal liquid NMR, although carbon 13 nmr was better than proton. The swollen samples from above are tested. The more crosslinked the sample, the wider the line was. We used the half height NMR command, but many manuals suggest using baseline width. This is especially good for polymer blends.
While you are talking about NMR, you maybe able to do endgroup analysis. This was done mostly with small polymers.
Never were able to get a good method by IR, although it was tried many times.
Good luck.