If you’re willing to strip everything off the top side the cleaning will go much faster. It wouldn’t surprise me if there was significant rust.

I’ve used simple green on a rag. You want to avoid water soaking into the wood. Ideally your method will only loosen the dirt and leave the finish untouched. A mostly impossible goal but that’s the idea.

Once you get that thick layer of grime off you’ll be able to make an informed decision on what’s next.

I’d start with whatever you have on hand. Alcohol, naphtha, Novus. Don’t grind the dirt in, loosen it and remove it with your rag.

Novus for those.