Voragh:
Yes, you can use {-pu'} with {-DI'} but it's not common. In fact, I could only find one example:
'uQ wISoppu'DI' maja'chuq We will talk after dinner. (PK)
You can also use {-ta'} with {-DI'} :
lojmItDaj veghta'DI' jubbe'wI' yInqa'meH chegh 'e' botnIS qotar qeylIS HoHmeH qotar qeylIS SamnIS Still, Kotar cannot let a mortal Pass his gates and return alive, Kahless must be hunted down and killed. (PB)
QIStaq 'emDaq jenchoH jul, yor DungDaq Salta'DI' tagh HarghchuqmeH poH The sun rises high behind the Kri'stak, When it rises over its top, It is time to do battle. (PB)
I couldn't find any examples of {-pa'} with a Type 7 aspect suffix however.
Thank you very much for this helpful information! If I understand you correctly, these are all canonical examples with *-DI'* and a perfective suffix, not just those that relate to the present / future? I mean, there is no canon of *-DI'* or *-pa'* with a perfective suffix, but in a past context? Are the canonical examples in the past always without perfective suffix? Thank you again!