Danny, get some of the new PE driver gasket - it's like the gasket foam tape at HD and Lowes, but actually better. For those cabinets, I suggest a length of aluminum channel (HD/Lowes) epoxied to the inside sides and back (off center) - completely different stiffness than MDF or plywood and you might be pleasantly surprised - then get rid of that misplaced factory brace.
Regarding PE, I can tell you that the majority of the orders I have placed/tried to place over the past year have had "stock outs".
But, PE is still a good source, so I'll get over it.