
I think mashed potato is the way to go for dogs that can't tolerate rice or wheat.
A vet nurse friend suggested Readybrek made up with water, it's just instant oat flakes with no salt or sugar added, it may suit wheat intolerant dogs better as oat gluten is slightly different.
With rice, look out for places that sell rice flakes/flaked rice [I think the Co-Op still sell it] as it's fairly instant and gives you the sloppy porridgy effect you need - microwave rice and quick-cook long grain isn't really soft enough and may well pass straight through.