You should also put an unun/choke on the feed line at the back side of your plate to ensure that only the plate and not the plate+coax+analyzer are involved. Once you've done that, I see no reason why your proposed measurement strategy wouldn't work to give you a repeatable number.
Of course, that number won't exactly reflect the antenna's behavior in actual operation, because even if your metal plate happens to match one particular HT+arm+body configuration it won't match others. You could have several different fixtures to model different situations, but even then you have the problem of validating your model.
The only way I can see to do that validation is to measure the reflected power in the real configuration — i.e. either a handheld radio with a suitable meter built-in, a physically compact meter inserted in-line at the antenna port, or an analyzer in a handheld form factor.
If you don't have this reference, then you can still make repeatable measurements, but you don't know what measured values correspond to the best real-world performance.
For what it's worth, some rough measurements about the size of the variation:
I have a handheld antenna analyzer which can read R, X, SWR, and return loss. The primary way in which it is different from a handheld radio is a very different case design (large and plastic rather than small and coated metal), which affects the amount of coupling to the hand.
I attached a 1/4 wave whip (no additional ground plane) and measured return loss values between 3 and 6 dB at 146 MHz depending on how I held the unit.
A more “rubber duck” style antenna (about half length) varied between 10 and 35 dB and was much more obviously sensitive to exact positioning.