A reconsideration of value is real and it's a formal, documented channel. It goes through the lender, or the AMC the lender used, not through a phone call to the appraiser. The lender passes your material to the appraiser, the appraiser reviews it and either revises the report or writes up why the original conclusion stands.
What the independence rules prohibit is pressure. Nobody with a financial interest in the deal may ask an appraiser to hit a number, imply future work depends on the value, or coach the conclusion. Giving the appraiser factual information they may not have had is a different act, and it's exactly what the ROV process exists for. The details of how that's handled vary by lender and by state, so ask the loan officer for their written ROV procedure before sending anything.
What actually moves the needle: closed sales, with dates, addresses and enough detail to show they're more similar than what was used. Pending sales and your own opinion of the arterial road generally don't. If your better comps closed after the appraiser's effective date they may not be usable at all.
One thing to sort out before you spend a week on this. The appraisal belongs to the lender and the borrower paid for it, so as the seller you often can't file the ROV yourself. You hand your comps to the buyer's side and they submit it. And be ready for the answer to be no. A large share of ROVs come back with the value unchanged, which leaves you renegotiating, the buyer bringing cash to cover the gap, or the buyer changing lenders and starting a fresh appraisal at their own cost.