Worm castings are great, and if that's all you can get, it's going to work fine (they're not great at fertilization, however, so you'll still have to do some of that).

They can be applied any time.

I love worm castings, they work almost as fast as the liquid fish fertilizer. My problem has always been finding them in sufficient quantities, as the bags I can get are only a pound or 2, soil mender brand. They don't go thru the spreader well either, so I end up walking around the yard with a bag of worm poo & a wooden spoon, tossing out small amounts as evenly as I can. My neighbors must think I'm nuts & probably warn their children to stay away! I use 2 scoops each on my roses & 3 scoops for all my hanging plants to help them hold water. Sunshine in a bag!

I can get a truck bed full for about $35 I plan so either sling it out with a manure shovel or dump and rake.

My secondary question is should I apply it now in a stressed environment or wait till fall and dump, rake overseed, rake done??

I can't imagine any reason to wait