I have the same situation, but since I have about 7 stealth accounts, I'll let you in one of the accounts, I'm doing.
I got the same message with PayPal for my SSN or EIN. When I chose to give EIN, they gave me the two options you mentioned.
I didn't want to call PayPal through resolution center, so instead I created a new email address and account.
It is EXACTLY like starting from scratch and setting up a new PayPal account from scratch. Once you get your email set up (if you haven't already), you have to have your email confirmed by email. You will have to re-set up a bank account link. Paypal has changed the rules in the last year in the sense that two paypal accounts can be linked to the same bank account if one is a personal account and one is a business account.
After a few days, just to be safe, I deleted the bank account from my initial personal account.
I will say when you submit your EIN #, during the process, PayPal does ask for a name and the last 4 numbers of your SSN to verify. That was a surprise to me, but I did submit genuine info.
Once my email was confirmed and bank account verified, you have to make sure the new email address is changed onto your eBay account so that it could process payments correctly--going into the "new" business account instead of your "old" personal account.
My EIN was in a different state than my registered eBay account, but I am using a
VPN. I'm in California, but my Ebay account is registered with an Arizona address.
I will say that a few days later, I did change my eBay account address to have a California shipping address. I do still use a
VPN that is based on a different state, but Ebay hasn't asked me about this, but if they do inquire, I will tell them that the California info is current, but I use a
VPN because I'm an internet gamer and I don't want other competitors to know where I'm really from. Because my address changed from Arizona to California, I already have a ready reply that I am a student and my AZ address is a permanent address of my folks and my California address is my college student location.
So far, so good. It's been a few days and I haven't been shut down on the eBay or PayPal side. Now we'll see if PayPal and Ebay are separate entities and if they share information, because my SSN might link this new account to my old information.
So that is the risk you will have to take if you go the "create a new email and account" route.
It is akin to starting a PayPal account from scratch and making sure it links to an existing eBay account of which you're going to have to link them.
If my eBay account become limited, I'll let this board know.
PAYPAL will not accept my EIN 
