im pretty sure it is only an open diff only one tire drives
IMO, that's not proof that you don't have a G80. My G80 used to allow one wheel peals all the time. I got a good feel for when mine would and wouldn't lock up. I've seen some reports from people who can't get their G80 to lock at all. Where there is already damage to the carrier internals, it's possible the locking mechanism is also damaged. Take 30 seconds and check the RPO sticker in your glove box to see if there's a G80 code there.
One of the weak points on the 10 bolt is the carrier, so I wouldn't be too surprised to see people reporting breaking the carrier when using a lunchbox locker.
Which Eaton posi is he suggesting? I would expect he is referring to the eaton clutch type limited slip, which is a decent unit and rebuildable (important with a clutch type LS so you can replace the clutches when they wear out). Just want to be sure, because Eaton makes lockers and other traction aids (including the stock G80 gov-lock). I personally don't like the term "posi" because too many people use it as a generic term for any differential traction aid (LS, locker or spool).
Assuming it's the Eaton LS, then, the part may be the same price as the lunchbox locker, but installation will likely be a lot more. Any time you replace the carrier, you have to set up the gears, which is a tedious task that adds to the cost. Usually you can install a lunchbox locker a lot easier than anything that replaces the carrier.
While we're talking about cost, if you have an open carrier, and the carrier itself is undamaged, it shouldn't be very expensive to replace just the spider gears. In terms of cost, that will be by far the cheapest option. But it all depends on what you really want to get out of this repair.