Armageddon Gear ultralight shooting mat and a separate molle bag is the closest I can think of but it lacks some features and weighs more before adding a bag.
That seems like a poor shooting mat as far as coverage if you are not a smaller guy. It would just BARELY let me get hips on it under ideal conditions. Would be nice to have an unpadded additional 12-16" to let your kness get on some straight nylon to protect from thorns, stickers, sharp sticks/rocks, etc.
Eberlestock has a full length, full width, but padded only down the middle field shooting mat, but it has to strap on like a Thermarest pad and you would have to add velcro for datacards.
Eberlestock has a straight up molle attach shooting rest, but you dont get the light multipurpose thing going with it.
Everything else is unpadded or just too big/heavy for what you seem to be looking for.