Actually, I see two ways to manage the classes "issue":
1- In NG+ you can't change your class (that would require a fresh start, it's the way Mass Effect 3 managed it and was fine to me). Probably the easisest way to implement this and would increase replayability, probably.
2- Add an item such as the Golden Nug. Every time you find a weapon, armor etc in NG, NG+ and following playthroughs is saved there. So I do NG as a warrior, then NG+ starts as a rogue, all my warrior only equipment is "stashed" and I have to find the rogue gear, clear the game then I do NG++ as mage, same thing (rogue gear is stashed). If I start a NG+++ and switch class again my mage gear is stashed and warrior gear is "unstashed" and added automatically when you interact with the Golden Nug after game start.
Same for the skill tree, it saves the amount of skill points I invested into it, then when I start a NG+ the tree is reset and I need to acquire those new skills again (kinda like a respec and that would allow me to "transfer" my skill points between different classes and avoid issues due to them haivng different skills).
The above is for class dependant gear and skills (all other items such as runes, materials, compainion gear etc are transferred between different classes across plythroughs).
This is obviously harder to implement but, probably, is the best user experience.
P.S: some gear could be missable due to some areas being visited only once. In that case, adding a merchant that sells that missed gear would be great too.