Author, I think I've found a nice batch of fridge horror sitting about that you might want to incorporate. If so, this could qualify as the site's 2nd Apollyon class object.
If I read your oberview of the stages correctly, the SCP doesn't actually impact the actual value of pi until stage 2; at stage 1, pi is still actually 3.14etc, even if your calculations don't show it, right? Also, starting at stage 2, the SCP doesn't actually shrink spacetime within its area of influence (AoI), it just makes circles and spheres have less internal area/volume as dictitated by the new value of pi, yes?
So, what happens if we put this into practice?
At stage 2, we have a slight issue: the circumference for the SCP's AoI is "too large" for its diameter. So, either the circumference needs to shrink, or the diameter needs to increase. Since the SCP doesn't affect spacetime, I'm thinking it causes the diameter of the AoI to grow so that pi=3.
I say this because we have to remember that there's still an outside world that says that pi=3.14. The last time it had influence over the SCP's AoI, everything matched up. Once stage 2 hits, it no longer has any control over the value of pi inside the AoI. Logically speaking, until it gets an update (so to speak), the world at large might still think that the circumference of the AoI has the same value, which prevents the SCP from decreasing it. So, as noted before, to keep pi=3, it must increase the diameter. And once it wraps back around to stage 1, shit hits the fan.
There's no way to decrease the diameter after stage 1 starts again (once the value of pi returns to normal), since that would cause part of spacetime to be erased. So, to keep everything consistent, the the SCP's AoI increases by about 5.51%.
If the above makes no sense, what I'm trying to say is that every time the SCP goes through a round of stages, the area of influence grows by about 5% due to the interactions between it and the outside world. And, barring technology that follows Clarke's third law, there's nothing that we can theoretically do to stop the SCP from expanding to the point where it affects the entire observable universe. You'd have to write-in a weakness just to keep this thing at Keter.