We never did come to an answer before Xmas really got in the way. Our needs did restrict our options quite a lot.
Our grilling needs are limited to bacon & warming naan breads. For toast, we have a toaster.
Efficiency should be a literal ratio of useful energy produced divided by the energy put in. So it should be about oven insulation, but when it comes to grills, not heating the sides ought to be the trick, but that’s probably why it sucks.