Um, the polish products only work "so well." If the pits are deep, you can grind on the glass all day and only make a divot. See if a local glass service does this and get them to look at the windshield... If they don't seem willing to take it on, well, you were warned!

Some "filler" products work OK on small pits and seem to help the glare.

Rain-X is another wonderful product... won't fix pits but it seems to reduce the smaller ones a little with frequent application (must fill them slightly... Like once a month "frequent").

Yeah, those pumps are pretty wimpy and only have a little impeller in there. Must be primed to work, perhaps intake side has a pin-hole leak or the pump is just worn out. The valves may help but I wouldn't put a lot of faith in that solving the problem... Can't really hurt.

Missing my whole washer bottle and pump so I haven't even looked into repair products!

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Mike!