Most P'n'P clamp boards by raising the conveyor up so the board is held against an edge or clams on the top.
MYDATA raise a bracket with clamps on the inside of the coveyour. (Against an edge on the top.)
Normally you also have a plate with support pins that raises too.
Went out only two weeks ago to visit two local fab/assembly houses who've, I was told, could have ran a product variants for the company I work for. To find its all side-edge held up as on the pictures (not mine, btw). All assembled that way and reflowed the same. So much capability for boards! Both of those fabulous houses couldn't ensure flatness and hinted about 'randomness' :/ When asked about induced joint strain & stresses when mounting into enclosures during final assembly, both looked at me clueless and couldn't care less.
Haven't seen the new Year 2021 assembly lines, bet they are better equipped with flat belt conveying and platform/podium style assembly and induction heating?
Don't know what issues you have with your products or you are just trolling.
But panel warpage is normally a design or pcb manufacturing issue. (copper balance, stackup, moisture etc.)
A easy fix could be to use a thicker pcb.
Guess if you have some really thin sensitive stuff you could place them in a support pallet like you use in wave solder.
How will you transport dual side pcb's if not by the edges?
Most processes use support pins or a center support rail. Did you make room for this in you design?
Big boards will sag in the oven, but thats what the center support is for.
We have some big heavy boards we place vertically in racks right after they come out of the oven to avoid further sagging while cooling.
Maybe the 2022 smt line will mount boards vertical to match a Seica flying probe.
