I have the Adams backrest for my 2.5-yo daughter, riding on an Adams Trail-a-bike.
Sidebar: I'm only worried about her falling asleep because she's pure passenger, unable to pedal. My older daughter, on a tandem with kidback cranks similar to yours, can't fall asleep because she's constantly pedaling! So, I didn't worry even though she started at 3yo.
On her, the Adams is around the ribcage, not really around the waist. There's some adjustability based on where you clamp it, but I clamped it high to get the strap up, so that if she falls asleep she can't slump very far.
I'd still worry about her being asleep, though, and would pull over and wake her, let her walk around, etc.
I think if your daughter requires a sleep option for the rides you're doing, a full child seat is probably required. We had one on the back of our tandem, and it didn't interfere with the pedalling kid at first unless the child worked her feet out of the heel-cups and straps.
Let us know how your 22-mo old adjusts to pedaling in a team. My girl, starting at right around 36 mo took a while to get the hang of it, even through the was a champ pedaler on big-wheel and her training wheel bike.