Directly from ATF:

"Right now, we hope to bring the form 1 back soon, followed by the forms 2, 5 and 9 if the system holds up under an increased user burden. The forms 3 and 4 look to be down the road as ATF is exploring the creation of a new system for these forms (they were the two high-volume ones) – if that works, we would move the forms from the old system to the new."

That doesn't give us a specific timeline, but it does give us a road map. IMO, it does not make sense to hope that eForms will be up soon for Form 4 filing.