Rupert,
I can't speak to the gromet question, but your heater core always letting water through may be a simple adjustment. I can get you started, others will have to provide more detail.
1. Open the hood.
2. Remove the rubber cover over the heater core valve. This is on the driver's side, near the top of the firewall, and is about 3 inches across.
3. Here you can see the valve and the linkage rod that actuates it.
4. Move the dash board control all the way open and note the position of the linkage and valve.
5. Move the dash board control all the way closed and note the position of the linkage and valve.
6. Determine the adjustment required and correct.
You may be able to disconnect the valve from the control rod to manually close it. This is a good test to make sure you don't have a physical problem that prevents the valve from closing.
Disclaimer: I have never personally done this, I have just watched other perform adjustments on this valve through that access hole in the fire wall.
Others have written about removing this valve and cleaning it and replacing seals. Search the tech articles and discussion forum for more info. Others with actual experience can add more.
Thanks,
Rodd
Powell, Ohio, USA
1966 230SL, Euro, Auto, Leather, both tops
1994 E420