I quibble a little with your objections to "mass" is what the instrument
measures, in section (2). The main objection you state seems to be
with regard to the non-ideal nature of actual balances.
Do you have the same objections with an operational definition of
"mass" is what the "ideal" instrument measures. I consider that to be a
valid operational definition; even if the "ideal" operation is
unrealizable in practice.
In other words, is your objection (perhaps to strong a word), that an
operational definition should only use realizable operations?