If you have a wide, flat skewer and a deep roasting tin you can reproduce something akin to a shawarma or doner by cooking it balanced over the tin in a very hot oven, turning to crisp and cook through and slicing off the outermost layer as you go.† It is a bit raggedy, but the taste and texture are definitely comparable to a conventional upright gas heater.
I interleave lamb fat, pounded shoulder and spiced mince, secure and compress with an onion at each end and it works well enough.
This does sound like it will work. Do you think mayeb using the broiler and rotating it every so often will make for even a better result? Can you elaborate on the spiced mince and/or marinade you use?
I marinade the flattened slices of shoulder in milk, olive oil, onion juice, salt, pepper and sometimes some wild oregano if cooking a doner. If making a shawarma, the marinade is (of course) quite different: citrus zest, oil, cardamom, cloves etc. - can't quite remember exactly what, though it's written down somewhere.
As for the spiced mince, I guess I do something a bit like an adana kebab: cumin, coriander, pepper, chilli, often with some onion juice and crushed poached garlic.
I have tried with the broiler but prefer just using a hot oven as it cooks the underside by indirect heat at the same time and ensures the fat and mince cook through from the inside out (with the skewer conducting heat).