Put handstands in the front, always. Hip extension work can go in the front as well, if it's just activation work. If it's heavier stuff then integrate it earlier sometimes if its suffering.
I'd go with an easier version of pullups and dips at 3x5-8 or so.
Basically, you gotta prioritize what you want to get better quicker. Handstands, in general, once you adapt will be more skill work instead of strength so it won't have much effect on y our latter routine.
From there you need to decide what you want to get better the fastest (first exercise) and what you want to be lower on the totem poll.
I would work lower intensity for a bit because the strength is apparently draining you too much.