From what I read in a guide, it sounds like the EXP is applied before the components' multiplier additions or subtractions, which would suggest to me that you should add the low EXP, positive-multiplier components one or a few at a time to get a bit more marginal benefit from their EXP as you work up to a x3 multiplier, then use all the high EXP, negative-multiplier components in one go to get the x3 multiplier for all their EXP.

Does the multiplier stay with the item when you close the upgrade screen or does it start over at x1 each upgrade session?