Pick me
I didn't BREAK my tailbone exactly, but I cracked it (umm, would have been about 8-10 years ago I think) by slipping on a wet concrete doorstep. I had a c section with my son (emergency, not elective) but during the natural delivery of my daughter (4kg, so classed as pretty big) my tailbone did pop out of place and is still pretty sore. It hurt during labour, although not excruciatingly so, but I didn't notice it during pushing.
It has made sitting down for long periods of time breastfeeding pretty sore (TMI, especially if I'm a bit constipated), but you can combat this by using different positions (like feeding lying down for example) or sitting with a rolled up towel under your thighs. It's manageable.
Having had a c section though, it's pretty much as you described your recovery after your broken tailbone. It's major abdominal surgery, and it does affect every aspect of lower body movement. For the first few days in particular I couldn't walk or lift my baby myself. It was awful. At least after Addie I could walk around and get myself out of bed (and the risks of a c section, like the wound infection that kept me in hospital for a fortnight afterwards, are measurably much greater than a natural delivery).
My vote: go for a natural delivery (even if baby is supposedly largeish - scans are so inaccurate anyway). Try to avoid an epidural if you can so you know when the pressure is doing something really bad.
That said, if the idea of pushing past a bung tailbone completely terrifies you (I hadn't even thought about it before labour) then it could affect how effective your labour will be and maybe it would be more straightforward to go for the elective.
Hope that was some use anyway! Feel free to PM me if you have any questions