EG61 --while I'm sorry to hear of your problem, I must relay that in general individual service issues aren't a forum topic. As moderator I don't strictly enforce this, but the problem is that many issues are individual and we can't confirm what happened, what was said, and so on.
Here, some of what you relay appears to involve a verbal misunderstanding. I don't know what was said or not said, but I would think that a seven day power reserve issue would take at least two seven day periods to resolve: that is, once adjusted, the watch would need to be tested for seven days just by observation (and possibly beat and amplitude measurement during that period). What you may not understand is that most power reserve problems reflect themselves in the swing of the balance (amplitude) and that is measured by a machine called a Vibrograph. There is, with respect, something to monitor and the caseback need not open.
Two consecutive testing periods might be necessary. One can't tell what happens at the end of the cycle without witnessing that end.
While that testing would not be "invasive" the watch before that would have to be opened for adjustment. I cannot tell whether there was a misunderstanding in communication: many answers depend on how the question was phrased or understood.
The mechanical seven day power reserve really doesn't stop exactly at seven days (that is precisely at 168 hours). It can vary slightly. Nor is the watch really designed to be run down completely: at the end of the power reserve period timekeeping will get off due to decreases in amplitude: if it's getting run down, the watch should be manually wound and will work best at full power reserve.
I would suggest that technical questions are fine, but it serves little purpose here to complain. I sincerely hope that watch is or will be fixed to your satisfaction.