Well, I will tell you how we do ICF on a conventional footing in southern Oregon and perhaps that will give you some thoughts on how to proceed with your project...

First we form the footings on top of an engineered 3/4 minus rock pad. Then we secure 2x4s at the top center of the footing forms such that when the footing concrete is poured it will create a 1.5x3.5” channel that will interlock with the ICF wall concrete when it is poured. Then we drill holes into the 2x4s every 12” OC and place vertical rebar dowels that will extend 30” into the center of the ICF block cavities. Then we pour the footing. A couple of days after the footing pour, we remove the 2x4s and place 2” lengths of PVC pipe on the dowels that are used for capturing the bottom end of the 12” OC ICF vertical rebar that we will later place. Then we place the ICF blocks, horizontal rebar, and vertical rebar. Just prior to the pour, the walls are checked and trued up and the bottom of ICF blocks are spot foamed to the footing and the ICF walls are then poured using best practices. We are in a seismic area and we use more rebar and wider footings than in most places. We also like really strong ICF walls.

I wouldn’t think you would want to embed any wood in your footing/foundation. I think whatever you do, you don’t want create any point loads on the ICF wall where the pilings are located. ICF wall is only designed to have its load evenly distributed to the footing. It would probably be worth while to have a structural engineer help you with this.

I'm not familiar with building ICF walls on piles and void forms, but this sounds like it might be a good place to use Fastfoot footing form material and Fab-Form Monopour ICF support system that allows pouring walls and footings at the same time.

Take a look at this link: https://fab-form.com/fastfootMp/fastfootMpOverview.php

Just an idea, but if you placed the adjustable supports on the pile caps (not sure how large the caps are), then screw 1x4s along the outside of the forms to support and bridge between the piles. With piles on 7' centers, you could install 8' 1x4s just above the adjustable supports and staggering them to allow installation flush to the ICF form. You could also assemble and glue sections of your forms together before setting in place to make a more rigid form assembly, similar to several Fab-Form videos on you tube.

Have you completed this yet?

If not...sorry I'm about 6 weeks late seeing this

buy 4'x4' void form, cut it on the table saw to match the outside width of the ICF form you are using
Wrap it in heavy vapour barrier (Super Six in Canada, US - can't remember the name, but its thick yellow plastic put below slabs) and use Tuck Tape and seal it up
place it between the piles previously installed
rip 1/2" OSB same width as ICF blocks and place on top
Be sure to allow the top of the pile to be in contact with the concrete (Don't cover it with the void form or OSB, cut them around it)
Set your ICF block on top
Use ~12" rips of OSB on both sides of the ICF from the ground below the void form up the face of the ICF block, about 6" both sides and fasten to the ICF with screws
add kickers to the ICF as needed to get and keep it straight
Place the concrete into the ICF as per regular way, 24" is one lift, consolidate your concrete, top up where needed, trowel smooth and set anchor bolts (Sometimes need to be in prior to pour, check your local area)

Next day - remove the OSB on one side of the forms, all the way around, use a crow bar and garden rake, destroy the void form, pull it out, re-install the OSB - you won't get all the void form out but try and get as much as you can

You now have a 6" void to allow for expansion of the soil under your ICF wall, and in 2-10 years the OSB will rot out and some earth may enter the underside but presumably not enough to cause a problem

I know my answer is a bit late. Still, while finding professionals for smaller jobs can sometimes be a challenge, your dedication and research will pay off in the end. And remember, you can always seek guidance from various experts.