Had a TP jam also several years back when taking two grand daughters, one grand son, wife, and myself back to Virginia. So plugged up that it was solid a snake couldn't even get through it. After adding water and using a plunger it finally broke loose. Why everyone else was swimming at the lake grandpa was sweating his butt off trying to unclog the toilet. LOL. I purchased a clear back flush extension from "Camping World" to monitor the waste being dumped out.
I haven't tried the suggestion of the Milk Bath and Laundry soap trick yet, might just do that.