It shouldn't take too long really. Greens being the priority for every course will need special and intensive treatment. We normally cut our greens 6/7 times a week (ie nearly every day). Eight weeks green growth would probably be several inches high and would need to be cut shorter in stages to avoid stress and vulnerability to fungal infection. When cut to the required height (for this time of year) they may need spiking, dressing, fertilising, aerating, rolling etc. In other words, a quite a process. But I'd hazard a guess at two weeks. Fairways, tees, approaches and semi rough, whilst being a lot to cut, is manageable. Bunkers are easy.
Six greenkeepers and a small group of volunteers (working 7 days a week) should be able to bring the course up to a decent standard. Obviously the weather, as always, will have a say, but I expect you'll be back out in a fortnight +/- a few days.
Good luck!