I’ve played around with it a bit…
I can’t figure out how to work it into the shortcut, but I can separately run
qdbus org.kde.kded6 /kded org.kde.kded6.unloadModule "appmenu"
and then launch Resolve, load a project, and keyboard shortcuts work fine. Then I can just run
qdbus org.kde.kded6 /kded org.kde.kded6.loadModule "appmenu"
and the appmenu starts up again and the keyboard shortcuts work—although there is no appmenu for Resolve, meaning Timeline Settings and such are inaccessible.
EDIT: As long as I don’t run the second one till I close Resolve, the appmenu dropdowns still appear at the top of the Resolve window. So, while it is slightly clunky I have to run these two commands, it is a usable workaround!
Particularly if I add a couple of aliases to make these two unwieldy commands a bit easier…
In ~/.bashrc—
alias resolve_start='qdbus org.kde.kded6 /kded org.kde.kded6.unloadModule "appmenu"'
alias resolve_stop='qdbus org.kde.kded6 /kded org.kde.kded6.loadModule "appmenu"'
An imperfect, slightly janky, slightly clunky workaround, but a workaround nonetheless. 
Now, if only I could figure out a way to properly automate it so these commands run by themselves when I open and close Resolve like they were supposed to in your Exec= line, that would be just perfect, as far as workarounds go.