What can I fill a trench around my house with to avoid creating a drainage issue?
Below grade you should not be using EPS foam - that should be XPS (pink or blue, normally) - above grade EPS is fine. EPS is not waterproof, XPS is. You can also increase your subgrade insulation a bit by setting a sheet (or portion of a sheet) going flat or angled slightly downwards away from the house at the top of the footing.



If drainage is a concern (or even if it's not much of one) and you have the trench around the house dug, dig a trench away from the house to a lower point and place drainage tile (not usually actual tile these days - 3-4" perforated plastic pipe - the holes go down) around the footing and out to the lower point, and you'll have a solid drainage system in place. It's one of those things that should be done before the foundation is backfilled in the first place, as there will never be a cheaper time to do it, but rarely is. If filling with 16 grit sand, place filter fabric over the pipe to help keep the sand in place. Filter fabric is a good idea in general, but kind of critical with a sand fill. Pipe is already buried below the insulation, beside the footing, in the picture.

Unless it's going to be noticed by the authorities and cause you hassle for "illegally diverting rain water" (evidently happens in some areas) you might want to drain your foundation drains (and gutters, if any - otherwise it will mostly end up in the foundation drains) to a big buried tank (cistern) so you can use any water collected during the rest of the year, and only drain away the overflow, if any.