The tree would become shorter ... but should balance-out from the loss of it's recently expended energy and not send up a hundred ‘new shoots,’ as if this had been done while dormant.

Now seems like a good time, actually. Just try not to damage the remaining foliage when removing the higher branches.

I agree with Jafar. You can open the tree to diseases if you prune during our wet weather.  Wait till you have some dry weather on either side of the pruning. 

I think the most important thing to think about is if your tree is overbearing every year or just this year. There are techniques to return biennially overbearing trees to yearly bearing.  Cutting off a tall branch is generally not a problem.  Fruit trees usually don't grow very quickly.  If it's just this year, thinning is more in order.  I have had so many branches break off of my plum tree that I had to put it into a shady area of my yard. It still produces a lot of plums. It just hasn't broken branches like it did in full sun.

What variety of plum do you have?
John S
PDX OR