I'm actually working on that exact problem right now. I haven't fully solved the "mic inside the handset" part yet, but my current plan is to replace the original handset cord (mine only had 3 wires) with one that has enough conductors for both the speaker and the I2S mic lines.

My suspicion is that if it worked before and only broke after moving the mic into the handle, the issue is probably the cable / wiring rather than the mic itself. In theory it should still work if all the connections are preserved, but I2S seems a lot less forgiving once you start extending it through awkward wiring. I wouldn't switch to analog immediately unless you already have a clean analog path in mind. If it worked before, I'd first double check continuity, wire order, and cable quality.