As a general matter, if you are filing something by fax at the USPTO, you should be faxing it to the Central Fax Number at +1-571-273-8300. Keep in mind that there are quite a few things that you are not allowed to fax to the USPTO, for example the filing of a new patent application or the entry into the US national phase from a PCT application.
Several members of the EFS-Web listserv (which you should join if you have not already done so) have reminded me that in the special case of payment of an Issue Fee by fax, the best fax number to use is +1-571-273-2885. (See USPTO web site here and here.)
The USPTO does not, unfortunately, mention this on its “Filing documents during an outage” page.
Note as well that Form PTOL-85B has a Certificate of Transmission designed into the form. This will satisfy the requirements of 37 CFR § 1.8. Note that you will probably need to include Form 2038 if you are trying to pay the Issue Fee by fax, and note further that USPTO rules say that when you send in Form 2038 by fax, it is required to be ink-signed, not virgule-signed (in other words you are not allowed to use an S signature under 37 CFR § 1.4).
Keep in mind, too, that given the migration away from landlines and over to VOIP telephone lines, the use of facsimile (fax) is getting less and less reliable (WIPO for example is discontinuing incoming faxes because of this). It is unfortunate that USPTO continues to rely upon fax as its backup system in the event of a crash of EFS-Web.
During the last USPTO payments outage, we paid an issue fee by fax. That is when I came face to face with the July 2021 update to 37 CFR 1.4 that removed the subpart (e) exceptions. The exceptions to s-signatures in this subpart were essentially just OED correspondence and the PTO Form 2038.
So, as an update to your post above: now you _are_ allowed to use an S-signature for the PTO Form 2038.