I have been using Oxalic acid trickle in winter for 5 years and have not noticed any adverse effect on queens.
Mine average 3 seasons and the odd one makes it to 4.
Some new queens do get superseded after a month or two but I suspect virus or nosema in cases like this - and these ones in the summer have never encountered an Oxalic treatment.
I have not seen any serious evidence that long lived queens produce longer lived workers.
Beo Cooper marked 100 workers in summer and found some of them still alive after several months and he used this to argue that AMM produces longer lived workers than other races but he had no control group with any of the other subspecies of honeybees. I don't think that is anything other than anecdote.

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