If you have PDSOI then you do have BJTs available, they are
just lateral and may not be modeled. But if you have a BTS structure
(body tied to source) then when you stand it on its head,
body tied to drain, that device is also a C-B transdiode with likely
better linearity than your designed diodes. The downside
in my particular SOI technology is defectivity - 90% of the diodes
have one I-V curve, and the others scatter from it. So bandgap
yield would be compromised. We see better uniformity,
though poorer diode ideality across the current range, from
"real" diodes.
You basically just have to get all your gain, and no great offset,
from an explicit CMOS amplifier, is all.