Just get a few local contractors in there, have them evaluate the drainage, what needs to be done in and out to prevent future flooding, and everything else and get a few estimates and compare them apples to apples. Most local contractors know the region, especially companies who do basements, they will put you in the right direction.

Good luck

Will contractors charge money to assess the situation?

Some charge (but they will tell you ahead of time), but some companies who charge will credit the amount of the price if they get the job. Some provide free estimates.

How difficult is it for you to do the "patch" that will close off their weird drainage system? If it's easy (and reversible?), I'd do that and then wait to see if you still have a water problem. I have an unfinished basement that had rare flooding with very heavy rains, but I knew there were issues with moisture and drainage.... the house sits at the base of a hill, very near a creek, and the neighbor pumps their excess water toward my house. :( I had all the masonry problems corrected and gutters put in with some underground piping to lead the water away from the house. The last of the work was completed at the end of last October and so far all seems good. In the meanwhile, I just wanted to mention that I used indoor/outdoor rugs down there with no problems at all.

It wouldn't be reversible; I'd essentially cut out the exposed pipe and fill with concrete. They do have those inflatable foam stops for me to test. The people who built it really did it all wrong- used a french drain pipe with holes in it under the foundation. The alternative will be a contractor digging up the foundation of my home to properly route the pipe into the main sewer... which I want to avoid.