What a thicket the authors of {{package}} seem to have created for themselves by trying to get a licence to do things it wasn't designed to do, not least simultaneously requiring you to display their logo and forbidding you to do so.
I am persuaded by apsillers' excellent point above. AGPLv3 says in s7b that
for material you add to a covered work, you may ... [Require] preservation of specified reasonable legal notices or author attributions in that material or in the Appropriate Legal Notices displayed by works containing it
and defines "Appropriate Legal Notices" in s0 as
a convenient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License
It goes on to note in s13 that
if you modify the Program, your modified version must prominently offer all users interacting with it remotely through a computer network (if your version supports such interaction) an opportunity to receive the Corresponding Source of your version
Assuming that the app doesn't copy its own source into its output, what the AGPL doesn't say in s13 is that s7 reasonable legal notice and attribution preservation requirements apply to interactions over a network with the application; nor does s0 allow such requirements to be sneaked back in under cover of interactively displaying Appropriate Legal Notices. All s13 requires is that you prominently offer interacting users an opportunity to receive the source. If they choose to avail themselves of that, then s7 does require that certain notices are maintained in the source. The AGPL doesn't define "reasonable legal notices". We have addressed this question previously; I see no grounds there or elsewhere to think that promotional statements ("Powered by foo") may be defined as legal notices.
Since AGPLv3 s7 is clear that additional restrictions that don't satisfy s7 may be ignored or removed. I contend that since the s7e prohibition on trademark reuse is lawful and clearly expressed, it trumps the very questionable s7b requirement to display the logo, and thus that requirement may be ignored. In the absence of any clearly-identifiable legal notices in the current source, textual acknowledgement of the current authors clearly and prominently placed in the downloadable source of your application will fulfil your s7b requirements.
You might well choose also to give a more prominent acknowledgment to the original authors in the UI of your modified application, but the form of that is up to you, and if you decide to do so, it doesn't relieve you of your actual s7 obligations, supra.
As ever, if you're betting anything of worth on this view, take professional legal advice first.
