First, purpleheart is gorgeous wood. Good call. But tough to machine. Be sure to finish it with something to help it keep its color. Over time it will shift toward brown to some degree.
Measure carefully. Patience.
Use eyeballs. They are more accurate than you imagine.
Sleep on it.
Get some beeswax or paraffin to lube the slides. Apply liberally. Test fit. The wax will not only help things run smoothly, but will also tell you exactly where any fit-up problems are.
Sleep on it again.
If it doesn't work, try the following method:
Adjust with 8 lb. maul or sledgehammer.
Don't get frustrated. Looks like a peach in progress, and it should be beautiful when you get it all finished.