Your pump should have the old style cone valves
The replacement ball valves are Benz Part # MB 000-074-17-15
The start sol. on the pump does aid in start by moving the rack foward anytime the start circuit is energized, [ regardless of temp], but only with starter..nothing during run. You can check that with a test lamp or screw in pump rack just to verify it's operation. If you find that is not working, a fix would help in a better/faster start , but this would have nothing to do with your warm up running condition...
The warm up a/f mix is dependant on warm up thermo and you have found the mix to be lean . What you want is for the thermo to cut off intake air at the air filter intake port between 65C and 70C .. you can verify this by simply checking when it closes and checking your temp indicator when it does .. if it is not in range , shim changes will bring it into spec range. It is pre-determined at the factory how much a/f they want throughout the warm up temps [ declining as temp rises] and if the heat sensor is working, but out of temp range, [ +/-] you can not get correct warm up a/f mix as needed for that engine temp.
In you case , I would do this test for findings .. if this proves to be in spec/range , then [ due to your case of leaness ] you want to be sure no false air is leaking during the warm up .. suspicions here are the throttle plate not completely closed and other vac leaks [ I always plug the booster line when doing this type of work, just to take that possible out of the equation]
If anyone finds the same complaint, but richness caused [ vs lean], then a dirty pump intake filter is suspect.. an easy test here is to simply take the filter off as car is in the warm up range and see if the engine speeds up w/out the filter installed .. that would be filter confirmation .