I also liked to double lunge my last horse because she was small, and for her it was very effective to have the second rein under her rear, both for sending her forward and for getting her to use her rear end.
My current horse is too large and rambunctious for me to double lunge comfortably/safely, though we have done it in limited amounts. My vet recommended the Pessoa system for conditioning the topline after an injury, and the effect of the device seems similar to what I was able to achieve double lunging my other horse, but (a) it’s too expensive, and (b) it has so many ropes, I’m not sure I’d feel safe using it.
What ended up being a good fit for our situation was actually working over groundpoles and cavaletti in a chambon. He learned very quickly how to lift through his withers and engage his hind end. I was really surprised by this actually because he has a tendency under saddle to run onto his forehand – the cavaletti were essential to getting him to engage his whole topline for sure. We’d been doing walk/trot over groundpoles in hand for a few weeks first though. Without that, he might have tried to rush through instead of naturally half-halting and lifting his legs deliberately to get over them.
He never had a problem putting his head up and inverting, which would be the gadgety “quick fix” use of the chambon. I don’t have any experience with it in that setting, so am not totally comfortable recommending it for your situation. If your horse is sensitive to poll pressure, in particular, the chambon is not for you. Mine isn’t, but he does get tense in fixed sidereins because he can’t effectively use his neck to help balance himself like he can in the chambon. Maybe when he’s ready for more collected work we’ll try them again.
Vienna sidereins are a nice in-between. They have the forward/down sliding action of the chambon, but without the poll pressure. There is a limit to how much the neck can stretch outward though (like fixed sidereins). I have limited experience with them.
Fixed sidereins would be the standard option and if you already have them, it’s worth just starting there and experimenting with things like groundpoles to see if you can get what you want from him that way. You might also try using just an outside siderein and experimenting with configurations for the lunge line. I like to run the line through the bit and clip it to the saddle/surcingle, so the action is more like it would be if you were riding.