There's what's called side mount casters, where the plate is to the side and not on the top, so that should reduce your height profile.
But the main issue is going to be the weight clearance. Casters have a weight limit to what they can support, even if your locking them into place, just the weight of a person sitting on the bed would basically break/crush the caster, even a metal & poly one. So the small 2" clearance casters only generally have a weight limit of around 75lbs, give or take 25.
So that's the height issue.
Is there a width clearance that you can work with? Because with side-mounting casters, that could be a possible work around to give you bigger wheels with more weight support.
Also consider a low-profile box frame instead of a metal frame, just to avoid welding. I don't know exactly where'd you'd find one to buy, but I was once given a mattress set that had a box frame that was made out of 1x3" wood boards mortised together, laid flat like a picture frame or a door, with a canvas like frame stretched over it. It was just thick enough to sit inside the metal bedrails and didn't actually come over the top of the bedrail. Making one should be easy, and can be bulked up with steel plates to protect and hold the joints. That was for a twin/double mattress, so I'm not sure what extra framing for a large mattress that would require.
Have you considered an aluminum or steel appliance caster set? They're generally around $15-20 per a set of two, and have a weight clearance of 1200-2000lbs with the way they're configured, which has 16 wheels per caster. But they don't have a lock on them. With the steel set, you could possible hack them apart and just weld them into a metal frame as long as you have a top plate welded into place to carry the load. They don't list the height clearance,
To get around the lock issue(other than a block wedge), if you make your mattress frame into a box that your mattress would sit in, there's Floor Locks, they're meant to combine with something on a caster, and basically it's a leg that drops down on a lever, to hold something like an industrial tote in place. I'm sure if you look around, you'd be able to find one that would fit. But they can be expensive and prices vary wildly between sellers, by as much as 50$ and more, so googling it a worth the time. You can get bottom mount and side mounts, the smallest bottom mount I've found tho is just over 3 inchs tall. And once engaged, you can gain about 2 inchs of height. So if you can get a set in the front, and in the back, that would make certainly lock your bed into place.