There is no known TB turbine conversion - or indeed any other engine option.
However, if one did just that, the range would shrink to about 2/3 which would mean I would suddenly be doing a whole load of fuel stops, which I hate. The other day I flew to Valencia and back, landing with 39USG and 31USG respectively (full tank = 86.2). With a turbine knocking a 1/3 off, such a trip would be marginal, to say the least.
And the oxygen usage is huge at the high levels - a cannula simply won't work.
We really need a turbine which is a lot more efficient that the present ex-helicopter-market 450HP turbines. There is nothing even remotely on the horizon,
AFAIK.
Turbine conversions are not the perfect cure. FAA certification requirements normally force Vne to be artificially low; generally AIUI at the bottom of the yellow arc. The Jetprop has a Vne of (IIRC) 160kt which is even lower than my TB20 (189kt) and it makes sense only at FL270 when you get ~ 260kt TAS. I know a US dealer selling this stuff and he tells stories of "lots of working rivets" and "Vmo warning CBs pulled" on most of the planes he works on, suggesting perhaps that a lot of people do make rather more use of the power than the airframe was built for. If I was buying a Jetprop I would do some due diligence on the airframe year (specific reinforcements in the tail area).
I think the issue is that Vne is related primarily to control surface flutter, which is related directly to TAS (the actual airflow velocity) whereas Vne is actually marked on the ASI in terms of IAS. If one takes the airframe to a much higher altitude than it was originally tested for, the Vne figure (expressed as IAS) has to be reduced, but nobody will have done the complete re-certification to determine the safe upper limit.