Yes, there is a solution for this. The only you need to do is to have a http://www.uesp.net/wiki/Morrowind:Spells/Self_Dispel#Dispel effect in that enchanted ring.
I think this could work in a extravagant ring (60pts) - Dispel 100pts on self, Restore Attribute:Strength 20pts on self
In my previous games I always enchant a ring with all attributes and cast a Dispel (100pts on self) effect before I use my "
Shrine" ring
Whatever you choose you're gonna need a enchanter or you can boost your enchant skill through the spell "Fortify Enchant Skill" spell effect.