Not surprising. This is really no different than dealing with city rats or raccoons. (Which are probably also feasting in your compost pile at night, and you just haven't discovered them.)

Chemicals and poisons are also not a good solution because they are indiscriminate. Compost is a living ecosystem - if the critters die, the process stops. Not to mention the collateral damage risk to bees, birds, and pets.

Whether the pest is roaches, raccoons, rats or bears, the solution is the same: eliminate sources of food and habitat (i.e. your compost pile). You don't pile your trash in the alley - you put it in a plastic bin with a secure lid. If you want to compost you will have to use an enclosed composting system rather than an open pile - something like a tumbler or a barrel. Take a look at this discussion.

What kind of roaches are they? There are different types. One that lives in compost piles a lot (including mine, here in MO) is called a wood roach. They also like to get under the bark in my firewood piles, and in mulched areas. However they don't seem to come in the house to speak of. The German cockroaches are the ones that come up out of the drains and like to live in your house. The wood roaches are very thin bodied and lighter brown. Germans are thicker and darker brown.

I don't know of a good way to keep them out of the pile, so I just keep the compost at a distance from the house and let nature do its thing.

You could always try to eliminate your pile completely by trench composting your kitchen scraps and sheet compost the rest as mulch in the garden.

It sounds like this basically is sheet composting, 30 feet long and only 2 feet wide? That's not a pile. Maybe a very, very skinny windrow. I'm guessing that this material can't amass enough volume for hot composting but is rather undergoing a cold composting process. I am a well-known bug-lover but even I would quail at working with compost that was boiling with roaches. And with such a restricted area in which to garden (is this your only gardening area?) I would be reluctant to give up so much of it to a spread-out composting area.

I would suggest figuring out some way of reconfiguring the way you do your composting. Either an enclosed bin or barrel of some kind, like an off-ground plastic composter, in another location, or perhaps vermicomposting. I have an even tinier garden area than you do, so I have a worm bin in the basement instead of a compost pile.

I live in a rural town, and like tox above, we have a goodly number of American, and wood roaches. They never come in the house and love the firewood stacks. The moist logs at the bottom of a stack of firewood is not much different from a cold composting situation. So, first try to ID which roach. The German cockroach is the primary one that prefers the indoors. I've never seen one outside, but again, I'm in a rural area where there are lots of enemies to keep them in check. You can do a web search to see the difference.

Leave them alone, they are beneficial to a compost pile. Roaches are but one of hundreds of classes of insect that help decompose kitchen and garden waste turning it into compost. Anything you do to kill them will also kill the other beneficials.

They may be a benefit to the compost pile, but not to the neighbors. This roach metropolis is adjacent to public neighborhood space.