Weyerhaeuser Vail is of course the big tree farm in the unit, but there is some Port Blakely and DNR on the west side and USFS and SPI (West Fork) on the east side that hold plenty of deer. Not necessarily motorized access though.
I'd see if the guest pass is valid for you and anyone that would be allowed under your permit, or if guests are just considered the individual named. Either way, I think they allow two guest passes now, so worst case would just burn two slots for you and your kid. They're $100 each.
Wish Weyerhaeuser would sell their permits before the draws like other companies.