It sounds like whoever sided your house didn't use nails long enough to reach any sheathing. Hopefully when you remove this sheet insulation you'll find some. There should be some 'nailers' there somewhere. If not then these are what maybe needed to attach your new siding to. Good luck, and let us know what you find and how you solve it. You could ask these companies you've been talking to, to refer you to a siding company who has experience in siding timber frames. Jim