They're easy enough to get:

https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-n...

 

Yea, the last couple of years preparers that dont use an EIN have some issues EFiling their own return with their SSN as the TP and as the ERO but Ive never seen anyone with issues filing a client return like that.

Go back through the Paid Preparer information in the Options, are you sure nothing is missing?

Apply for one "for banking purposes" and stop giving out your SSN.

Did you enter your PTIN?  That should eliminate the need for the EIN.

I don't have my EIN entered on the tax returns I file, and it works fine.