Are there any features to look for when selecting a peel and stick membrane for a PERSIST style wall retrofit?

I’m planning to remove the siding from a section of my house and insulate with rigid foam on the exterior. My plan is to remove everything back to the board sheathing (tongue and groove ¾” material) and apply a peel and stick sheet membrane over the boards, then 2 layers of EPS foam and then furring strips.

I’m still uncertain about what to use for the membrane over the sheathing. I know there are various peel and stick membranes on the market including vapor permeable and impermeable options. At my local building supply store, I have found Bakor Eaveguard Self-Adhered Shingle Underlayment for about $0.30 /sq foot. This product is intended for roofs, and is made by Henry who also make the BlueSkin membrane. The Eavegaurd is “composed of high-tack rubberized asphalt and glass fiber mat” I certainly like the price, but I know there are more appropriate products for this application specifically made for walls. I’m wondering if it matters or what to look for in these products.

I’m dealing with solid board sheathing so there are some irregularities to cover, and it doesn’t need to be vapor permeable because it will get covered in 5-6 inches of EPS foam. Located in climate zone 6.

Link to the website for more details:
http://ca.henry.com/roofing/roof-underlayments/eaveguard-self-adhered-shingle-underlayment