Regarding the Vaseline...... I guess it depends on the type/level of butt burn you're suffering from.
If the affected area of skin is weeping, oozing, red raw and of similar 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 users will apply a layer of Vaseline on top and over the applied ilex to prevent the butt cheeks from sticking together or from sticking to underwear.
Personally, I've never experienced that kind or level of butt burn, so I've never need apply the ilex so liberally and in such a manner.
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; although l only become aware of this after a BM and during cleansing; which is easily overcome by use of a wet wipe to cleanse (wipe).
Sometimes, you may need to pinch clumps of dried ilex paste away between a wet wipe, but other than that, the ilex is easily removed with wet wipes & no need to use oil.
Once, ilex has been applied, best use wet wipes to cleanse after a BM at all times, as toilet paper will drag and rip.
Also, 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; for me, this made all the difference.
Has it been confirmed you're NOT actually suffering from Pouchitis ?