If it's only on long trips I would lean towards the cap anyway but since you said it "pushed out" some fluid - whether it was into the expansion bottle or out onto the rad itself - that seems like the culprit as it could allow the fluid to boil after a while when it gets hot enough.

Get a new cap.

If it were my car I'd flush the system again just to get any remaining gunk out of it - get the air out by removing the bleed bolt on the upper hose after you fill it (wait until no more bubbles) Next run the engine w/ the cap on the first stop position, not all the way closed, until the cooling fan comes on twice and then add coolant up the the top.

There's a couple other ways to make sure you get the air out of the system, some faster, but that's the by-the-book way for my '92 civic which is a very similar setup to your car.(same engine so prob. same rad)

Make sure your cooling fan works correctly before you run it w/ the cap 1/2 closed, otherwise watch the temp guage.