I understand the concern with a coolant leak, but I don't see where this has anything to do with your running problem.
If your shop doesn't want to invest the time on setting up your pump properly because they are afraid they will have to replace it for the housing leak, I would say to go for the performance fix first as I'm sure we could find a cover. I'm also sure I could fix your cover.
Bosch Master, ASE Master, L1
33 years MB technician