First make sure you have your livestock situated for several days to a week in the makeshift QT, provide as much of your filtration to it as possible, do not forget about heat. Be prepared to provide proper light on after day 3 (little to no light during the first 3 days should not have any serious impacts to your corals, and will help to keep fish stress down.
After that...
Rope Buckets, you can get a couple of the large ones, wash them out well, wash again with vinegar, rinse with RO/DI and then fill them with the sand. Keep the sand with water over it, cover the bucket to try and minimize evaporation, and cross your fingers!
Hopefully your tank fix will not take long but regardless you are going to minimally have a couple of mini cycles. Order some Dr Tim's One and Only, for when you start your tank back up.
You are also probably going to need some (1-2) extra heaters and power heads (1-2). Your current ones will be needed to keep your livestock alive, and once you have your tank fixed all that sand and water in you will need to warm it back up.
Once you have your tank back up with the sand and water and it is up to temp, I recommend you drip acclimate your makeshift QT with the DT, for several hours. Since the volumes of water are not small it is less drip and more lite controlled stream, with some process for taking excess water from the QT and putting it in to the DT. In the end you want them to blend 100% before moving your livestock back.
After that transfer everything back and keep your light levels really low for the first 12 hours before gently bringing them back up.
Good luck and let us know how you manage.