Had a look in passing today (in fact, met Moose up there) the road closure is an over-reaction, I think they have to cover themselves when something like this happens within so many feet of a public highway.
Access to the Giants driveway is still available from the Winnats direction for vehicles with a good steering lock, I would advise others (minibusses etc.) to approach from the Eldon Quarry direction, they are only plastic barriers which can be easily swung open, but make sure you close them again!
The hole itself is very interesting, I would put it about 20metres, (but there again Moose has surveyed it) a level goes off at the bottom, I didn't ask Moose what was at the end of it but it is likely to have an effect on the drainage of the Snelslow swallets if the depth could be attained.
I think the best solution would be to bridge the roadside section to allow the wall and drive to be finished, but leave a caver access on the off-road side to allow for further exploration.