I wouldn't trust some shitty casters from Lowes/HD either, it would need to be some good ones from
McMaster Carr.
I've looked at using a recliner at a desk too, but building a stable platform with proper spaced casters to set the chair on seemed rather difficult. Best case would be to wield up a metal platform, so it would be as close to the ground as possible.
IMO, a easier/better solution is mounting the monitors on long arms attached to the wall so you can easily move the monitor and use a rotating base on the recliner to easily get out of the chair.
Good durable casters aren't cheap. This is only a small representation of McMaster's selection:
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