I do not have any experience with putting used cat litter in a compost pile, but from your very! specific stated details I would say it would be safe (at least I would do it) and a good thing to put on your compost pile (plenty of nitrogen to help the cooking process).
You will want to balance out all that nitrogen with plenty of brown matter in your post pile. For brown matter there is nothing better than shredded, fallen Autumn (Fall) leaves, IMHO.
I would also make sure the compost pile is kept moist enough by adding water as needed.
Why do I say the above is safe?
With our second son we used compostable diapers. Pee-pee ones went straight on the compost pile. Poo-poo ones were emptied & flushed down the toilet (you never want to deliberately add fecal matter to a compost pile).
For what it is worth, Bob Flowerdew from BBC Gardeners’ Question Time podcast is constantly encouraging people (especially males) to pee in their compost pile, maybe not directly, but his point is, pee is wasted if it doesn't end up on the compost pile. Personally I haven't gone down that route...
Now the flip-side, below are (just) a few places that advise against putting cat litter in a compost pile:
Now that I may very well have gotten you even more confused on what to do for the best, I'd say it really is your choice to make one-way or the other...