2 more (Michelin) ideas:
275/80R20 XZL 37.0" equivalent to 10.5R20
325/85R16 XML 38.7" A bit wide for 6 or 7" wide rim, designed for 8-9" rim; but they have been successfully installed on narrower rims. I know these are readily available, at least in North America (we get less variety in Michelin military tires than Europe; for example 7.50R16 XZL is never seen here, and my 395/85R20 XZLs are hard but not impossible to find), in the slightly used state from surplus dealers.
The 325s (55kg) would be my second choice after the 11.00s(49kg). I have trouble believing that a European Michelin dealer can't come up with the 11.00s, but maybe so...
The 325s have a footprint only 4% bigger than the 11.00s. They do have a 100kph speed rating, but with your tiny load you could add 5 psi and safely go faster I am sure.
Charlie