Your description of the screeching noise on cold startup is probably the air pump as you had surmised. If you elect to replace the pump, you'll find that a new pump from the dealer is more than $1000! However, there is an option. When mine went bad, I did a search and found that Adsit stocks rebuilt air pumps. For my E320, the rebuilt pump was less than $300. And, you can order the pump over the internet.
Hope this helps.