I think the quickest and easiest fix for drainage, will be a sump and pump system.
there is two problems with this, one finding a suitable place for the sump, and not disturbing the footers by building it.
The most logical place for the sump is where the smiler roundel is, Lift it up make the sump and then use the roundel as a cover for it. but what would that do to the footers.
then cut shallow channels into the concrete floor to channel the water into the sump.
however i could be talking crud, as i am not a chartered engineer