The Vaseline...... I guess it depends on the type/level of butt burn you're suffering from.
If the affected area is weeping, oozing, red raw and of similar in appearance to a baby's diaper rash; then the ilex paste is best applied heavily and smeared over the affected area; when applied in such a manner, some will apply a layer of Vaseline on top and over the ilex to prevent the butt cheeks from sticking together or from sticking to underwear.
I've never experienced that kind of butt burn, so I've never applied the ilex so liberally.
When suffering from anal itching, fissures or a burning sensation, only a small pea size amount of ilex paste is required and applied; yeah the butt cheeks will stick together and the affected area will feel a little crusty but you'll only notice after a BM and during cleansing, which is easily overcome by use of a wet wipe to cleanse (wipe).
ilex is easily removed with wet wipes & no need to use baby oil.
It's best to use wet wipes, as toilet paper will drag and rip.
As you're experiencing 13 BM during a day, rather than wipe both cheeks together, front to back; try wiping (with a wet wipe) each cheek separately, one side at time, changing hands. to wipe side to side from the middle outward; this will make all the difference.
Has it been confirmed you're NOT actually suffering from Pouchitis ?