One contractor has as part of his estimate laying pavers to the edge of the original concrete--which means removing the bottom rail of the aluminum pool cage and replacing it over the new layer of pavers, then replacing the screen...
To me this seems parallel to laying tile or wood flooring and removing baseboards or built in appliances like a dishwasher or trash compactor--and laying flooring then replacing the appliances--to make new flooring flush to wall surface
It is a finished look...

But the other contractors and some of the people I have talked to who had their patios resurfaced with pavers only have them run up to the bottom of the pool cage...so they are about even with that bottom rail...

Any comments one way or the other?
I am going to call some companies that do pool cages and see if there is structural reason to take it up and replace on top of pavers...
it doesn't have to be done by a pool cage contractor--no license to just raise it basically...I called Sarasota county permit dept today...

appreciate any info

The second he learned about by word-of-mouth. He went around to his neighbors and checked out their lanais. The ones that he liked, he asked for the name of the contractor. Two or three houses used the same crew and that's who he went with. It was a little more expensive than the first guy (almost double when you consider this was a SECOND remodel), but the final product was much better. It might seem weird to go around knocking on doors saying, "Do you have your lanai paved? Can I see it?", I know I would have a hard time doing it, but in the long run, you meet your neighbors and you could end up with a lanai remodel that you actually like.

any input as to using polymeric sand vs loose sand as top dressing for pavers
One company said they did not use it
others do.

apparently when pool cages are put together the bottom rail is screwed into the concrete--which we can see...
and there is L bracket in corners of the uprights and the bottom rail...
but there is also INSIDE the upright at least one screw holding the bottom rail to the concrete patio...

So the guy asked me how they were going to take off that bottom section and I said unscrew the screws and use new ones when they put it back...
he said yes--but if they just break off the interior screw they likely will damage the bottom rail and void the structural integrity of the pool cage...

He said to do it correctly you have to open up the upright aluminum post to get to all the screws holding the bottom rail to the concrete...very time consuming so very expensive...

I said so you wouldn't really do that unless you were redoing the pool cage at same time and he said 'that's right"...

SO guess I will contact the guy who says he would remove the aluminum strips and replace and ask how that is going to happen...

live and learn...

Find the stone paver you like and look to the distributor or manufacturer......they will have a list of preferred installers but can also provide installation details that are approved

Personally I think you're looking for a glue-down installation like tile.....with overlays the weak links are always how-to-handle the transitions and doorways

Don't mess with the structure......My-Not-So-Humble-Opinion

agree that finding a paver might have been the first step vs finding the contractor
but most paver suppliers in FL are local--meaning you have to be here to see the product..
I was in DFW TX area when my husband first started this project--
his idea to get the patio redone although he has spent 10 vs my 110% of time researching and planning what he wants...
so we got names of contractors from our realtor who has given us really good electrician and whose judgement we trust...so we could start the estimate process...