Schedule 7 of the 2023 Traffic Management Plan (linked at start of thread) refers to prohibiting a right turn from the A361 into A37 from 0800 on the Monday before the festival.
The right turn in question is required to get to East CV parking if you were to approach Eastbound from Glastonbury and through Pilton village. Although the main A361 Eastbound through the village may itself be open you may find that on reaching the junction you were then forced to take a left turn towards Shepton Mallet, and to then do a 360 at the next island to then head south down the A37 (past the junction you've just turned left at ...) towards East CV access.
This would not be a significant diversion and assuming light traffic on Tuesday would be feasible for you
Your alternative idea of heading South East to Baltonsborough to then join A37 northbound would also be feasible as this route is not subject to any closures, but is a longer route.