Expected paver settlement on sand

There is a much easier way to accomplish what you want. Since you are compacting the gravel, it will not settle at all. The sand is only two inches thick, so if you compact the sand, it will not settle either. Simplest, best technique is to place and compact the gravel, then place a small area of sand, compact it, then place a couple of pavers so that the top of the paver is flush with the adjacent sidewalk (or perhaps 1/8 inch at most high). You can wiggle the pavers a little to get them to be exactly flush. Now you know how much sand you need, so place the same amount of sand over the rest of the gravel, install pavers, you are good.

It is not necessary to plate whack the pavers if you compact the sand first. In my experience, plate whacking the pavers risks breaking them, and all it does is indirectly compact the sand under the pavers (but you already compacted that sand, so it is not necessary).

I understand that the paver sites generally recommend running a plate compactor over the pavers. This is done to compact the sand beneath the pavers, obviously the pavers themselves do not compact, since they are concrete, brick or stone. When we did our walkway (brick), we compacted the sand, then placed the pavers. It worked fine, the walkway has been in place for 15 years, no settlement, no problems.

There is nothing wrong with compacting over the pavers, other than you might break a paver or two, but in your case you are trying to achieve a very specific goal, namely matching an existing walkway. If you are uncomfortable deviating from manufacturer's recommendations in this case, perhaps you can place the outer band of pavers (the ones that need to match) by compacting the sand first, and place the inner pavers by compacting with the plate compacter. I think you will find the end result is the same, but post if it turns out differently.

As an option, you can place a test line of pavers on uncompacted sand, then measure the compaction when you run over the pavers with the whacker. Once you know the compaction amount, you can set the sand grade appropriately.