Bacciagalupe

I'd add gravel bikes to your list. Many have similar (if not identical) geometry to endurance bikes. They tend to have lots of mount points for racks, fenders and bottle cages. A few (like the Specialized Diverge, or the higher-end Canyon Grail) have mild suspension options.

I'm not planning anything quite as ambitious as PBP, but I'm currently bouncing between my Roubaix (carbon, rim brakes, max clearance 28mm) and Diverge (aluminum, disc, Future Shock, 32s). They have the same fit without going to any extremes. I'm still experimenting but it seems like these two bikes offer the same speed and comfort performance. The Diverge is a little more flexible and a little less precious as well.

By the way, the Specialized "Future Shock 2.0" (i.e. latest version) is a suspension headset that can be adjusted on the fly with a dial. This could work well for you, but you'd have to find out if FS can handle the additional weight of aero bars. Also, keep in mind that the 1.5 version isn't adjustable on the fly.

That said, given your fit and health constraints, you might want to consider... dare I say it... a custom frame designed in collaboration with a pro fitter. That may be your best shot to get the right geometry and aerobar setup.