I just replaced a front assembly with the home button connector so stiffly attached that the tab to the left of it broke off while trying to lift it. This happened while resting the display on a very hot iOpener. Some phones simply have a much stronger adhesive. My only advice is to gently prod at the connector from the left with the sharp pointy end of a spudger until it eventually comes lose. In this situation, I was eventually able to lift the connector off undamaged, but I feel like it could've been easier the way you've mentioned, by keeping the two parts of the connector together!
+1 for a photo showing the correct layering and routing of cables. I accidentally routed the home button ribbon above the digitizer ribbon and beneath the power and backlight ribbons. The uneven pressure it put on the digitizer connector after tightening the plate caused my digitizer to not recognize touching the display or made touches appear off center.
This was by far the hardest part of the repair for me. Getting leverage while finding a way to prod with a spudger is a challenge in coordination. I used a second spudger with point holding the phone down by the headphone jack, with the other end of the spudger anchored to my desk.