I found some handles that attach behind a monitor leveraging the existing mount. (Handles exist is my point, so I don't know if the link I provided has the best prices.)
Rear mounted handles would negate the need to invest in hardened LCDs, me thinks. With the arms that others suggested, these handles look neat.
https://www.ergomart.com/components-guide/arm-adjustment-handles
A monitor cable extension and the creative use of zip ties could allow for frequent moment, like you described. Retractable monitor cables I found look most bad quality.