Hst can work well for cutting, but I would make some modifications. Don't do an SD while cutting, for one. Instead of doing the 15s during the first two weeks, you should start with the 10s or even the 5s, so you can get into the heavier weights. Do the 15s interspersed with the 5s, so you do 5s MWF, then 15s TTHF. Don't use high volume, don't use isolations very much. Stick to compounds and only a couple sets for each exercise.
If you need to do this for quite a while, then you can extend it for a long time using various techniques. You may not be able to handle as much weight, so be prepared to cut back if necessary. I would only increment every third workout. Do negatives if possible, after you've done the 5s.