These American cockroaches (aka Palmetto bugs) actually prefer the outside rather than inside, but will gladly seek shelter in a home that has access, food, and water. As you can imagine, they are NOT fun housemates, lol.

I'd do all that you can do to make certain that there are no tiny openings around the house for them to squirm through. It might be worthwhile to add some food grade diotamaceous earth to the pile.

I like the diotamaceous earth idea,
but worry that it would do in any earthworms I might eventually develop

I should have mentioned that the compost pile is located a long way from anyone's house
(And that around here, there's not much hope of avoiding an occasional palmetto bug in the house)

Most expert sources say that DE won't harm earthworms, probably because of the layer of slime they surround themselves with.

When I lived in Coastal SC (American Cockroach Country!), I used DE in the dark nooks and crannies of my house, porches, and garage. I somehow managed to escape having them inside, but sure did see loads of them hanging around the outside.

Thanks!
Sounds like I've got a plan for the compost pile, then
(Plus a few other local trouble spots as well)

Oops... Just did a Google search and found this:
http://forums2.gardenweb.com/forums/load/soil/msg0916461518255.html

Bottom line--cockroaches in the compost are sorta helpful,
I shouldn't mess with it

But I'm glad to know about the DE,
I'll be using it around the house