Oh man that sucks!
Crawlspaces are horrible.
The sump pump would be the answer if you can't get it to drain out the foundation wall somewhere.
We just did this for my aunt. In fact it was so bad she lost a bathroom floor....rotted out.
NOw she has this soil that they call Gumbo down here. It's very hydronic. We took a 4" pvc pipe and ran it in under the foundation wall (there is absolutely NO WAY to get in there and do a sump pump or put gravel down).
THe dirt (mud) under the house was channeled to allow the flow of water to this pipe. It's not perforated pipe, it's solid - we then tied in the downspouts and ran the pipe all the way out to the ditch. We backfilled the entire ditch with gravel to act like a "french drain".
This soil is so wet all the time - no lie - you can't walk out in the yard at night cause the crawfish run the yard and they'll snap a toe or two. Yep they live in the darn yard. Buried during the day, roam at night. Sorta gross.
Good luck and have fun!