Create two new instances (DV2, QS2) as copies of DV and QS. Apply support pack to DV, and then QS.
Urgent fixes are applied in DV2 and transported to QS2 and thence P.
The same transports are also put into DV and to QS.
DV2->QS2->P
DV2->DV->QS
Alternatively, only make QS2, but open that system to changes. The transport routes are
QS2->P
QS2->DV->QS
As a final step, when you apply the packs to P, you can import into P the transports that have gone to QS. This is essential if the fix in DV2 isn't identical to the fix in DV due to support pack levels.