FYI this happened to me last time there was a $180/200 sale. I talked with a customer rep (online chat) and they said the membership limit resets every 30 days. Hard limit, no exceptions since it's same SKU they use for the eGCs on the website.
For my case I already reached my limit a couple weeks before the sale. I talked with a rep during the doorbuster and they said they would honor the doorbuster once my limit resets, even if the doorbuster has ended. They gave me a incident number.
So once my limit reset, I purchased 4 eGC's at the regular $190/200 price than I talked with a rep and gave the incident number and got a $40 credit back to my CC of payment. Bit of a hassle but it worked. It's worth a try on May 2 once the doorbuster starts.