and it works really nice even with the big ol' chipped flute from pulling out and slamming into the bed of the lathe haha.
I honestly don't know how that could possibly have come all the way out of the holder without at least
destroying the collet. Are you sure
nothing besides the endmill has been damaged?
I have seen lots of "my endmill pulled out of my ER collet" threads in here over the years, and more often that not - perhaps exclusively - it's from American members using inch tools. Are you using a high quality brand name collet with true inch nominal sized bore? Lots of "budget" inch sized ER collets are remarked metric collets at the closest size.
The difference in grip on a 5/8" shank between a true 5/8" bore collet and a collapsed 16mm bore collet is very significant.
Here in metric land there are standards for shank sizes and collet bores, so a correct fit is mostly guaranteed, and it's not so easy to pull a tool out of an ER collet when the fit is correct and precise. Imperial collets and shanks are not so well standardised or controlled IME, but the odds of getting it right are improved by not buying cheap.
As you are using Sandvik - they have a series of high quality true inch sized ER collets. Maybe get one of those if you are not already using something like that.
When you are assembling, after cleaning everything thoroughly, put some light oil on the nut and the collet seat, but not
on the collet or the tool. That alone makes a big difference to the collet drawing in properly.
Other than that, a long series 5/8" endmill with full length of engagement is pushing the limits of ER32. If nothing else works, going slower is all you can do.
As others have noted, live tools in general require some form of external cooling if running for any real duration. Get some coolant pointed at the body of the holder.