Hello, Brandon. You typed class D in your subject but then stated KPIE a class C, so I presume that "class C" is simply a typo and that you meant that KPIE is a class D, which it is.
In looking at the airport information I see that runway 16 is a left traffic while runway 34 is right traffic. It is apparent that the FAA wanted to keep aircraft out of that class D as best as possible, given the two to three mile distance between the traffic pattern and the class D airspace.
Based on my experience of flying in the northeast US my first thought would be to call the KPIE tower on a landline prior to flying (during flight planning and exploration) and ask them about the scenario of needing to clip the class D airspace (call mgr via AirNav listing and ask for tower number). What do they recommend and what have others done in the past?
An extended downwind on runway 16 would indeed put you into their class D airspace for the base leg and without prior contact would technically be against the regs. In other words, I do not believe there is any acceptable margin and the FAA would be all over that violation, especially these days.
In many cases, an extended downwind is not something you know you need in advance; instead it is a decision you make based on unfolding circumstances while on the downwind - most times , for example, it is due to the aircraft in front of you thinking they need to fly into the next zip code before turning base. Hence, I don't see there being a lot of time to call PIE tower to make the required contact when you have time to discuss it. I would also be concerned with the workload of a downwind-to-base-to-final phase of flight coupled with an attempt to make contact with the tower. Can you say gear-up landing?
If I were in the pattern and discovered at the last minute I needed to extend the downwind I would probably bug out of the traffic pattern to the west and rejoin, rather than scramble to contact the tower.
In addition to calling the tower I would also consider calling the local FBO during flight planning and ask to speak to a local flight instructor/pilot about that scenario. What is their experience and recommendation? Many times when I fly to an unfamiliar airport that has "interesting characteristics" I will do this just so I have a local's input.
In sitting comfortably at my desk (rather than in the hot seat of the left seat) I also believe that a prudent pilot would put monitor KPIE tower along with Unicom prior to entering the KCLW traffic pattern.
Some food for thought unless/until a local from that area could provide better ideas.