The big issue with Turbocharging in a Morgan is going to be the heat problem, and this will come in two aspects.
One is that turbo engines generally require a larger capacity cooling system as, even with an intercooler, the inlet charge is at a higher temperature so the whole gas cycle runs hotter, and this requires more cooling.
The second, and in my opinion the more important for a trad Morgan, is where to mount the turbo so it does not heat up either the engine bay, or any surrounding bodywork.
I too prefer supercharging, and ran my +4 with a blower for a period. Despite great low down performance it was beset with heat problems, and it never gave the top end grunt I was looking for. Ditching it and going back to high compressions and 2 twin choke Webers was one of my better decisions.