I did a model and started at 265" inches as you noted. I ended up with 269.7" inches in length tuned using 108" radials however. I could not get the 52"L x 13"D coil to work and show a good match at 27.205 MHz, the antenna was too short and needed more inductance.
I cannot explain this rather large difference in results, but maybe the large plate you had your radials attached to made the difference...that is like a large hub which I did not model.
I tried making the 4" element between the radials and the coil larger and it did improve the model, but I ran into geometry errors before I could get the model to show a good match at resonance. I did not want to take the time to try and model your radial hub plate.
Plus I think your isolation of the bottom of the radiator inside the support and mounting bracket also adds some capacitance I cannot duplicate.
The antenna model shows very good low angle gain and a good match tuned with a 22.5' foot radiator and mounted at 36' feet with my coil at 66"L x .50" diameter tubing and 8" inch legs to this helix axis. However, the band width is pretty narrow covering only a little over the CB band at <2.00:1 SWR so that should provide about as much gain as possible if the old stories about narrow bandwidths is true and easy to determine just using a radio.
The model also shows some CMC on the mast and I did not Isolate the mast or add a choke, but you probably took care of that.
That said however, if I was able to eliminate some of the CMC noted here with either method a choke or isolation...the model would likely show a little less gain as a result.
Keep us posted.