Maybe I'm not understanding what you have in mind but your drawing looks really complicated with sliding rollers in captive grooves and such. I also imagine the lateral movement when weighing something is undesired. I would just try to shove something underneath.
Simple methods are vertical guide rails that can be pinned. Or a swinging beam with a radiused top or eccentric cam that can be flipped up and locked/pinned into place.
But in my opinion, your thought about screws is the best. By far the most secure and with the greatest leverage. Use one in the form of a screw jack and use a multi-start thread to make it faster. That will solve the speed issue. You'll need to find someone with a lathe to single-point thread you some, which means instead of screws you might as well get them to just make two big screw jacks with hand crank wheels, instead of four smaller, regular screws.
Or if you can't find someone with a lathe, then perhaps find
multi-start/fast travel threaded rod or lead screws. Typically used for linear motion.
If your plate was being guided on vertical tight rails then you only need one screw jack if it is big and strong enough since the rails would eliminate tilting.