OK, I'm not sure what the trouble may be. It seems to be running OK, and I've just been playing an exhibition game in the park with no obvious issues.
I uploaded a freshly-compressed version of the park, let's see if this helps:
Latest attempt at Messer Street Grounds. There's one very small change where I updated the mtl and texture folders, but it was working fine for me before then so I don't think that would be the problem? In any case, I got rid of the download link above. Before installing the new zip file I guess I'd nuke the site from orbit (or maybe just delete the old folder), since it's the only way to be sure.