I find it hard to believe that you will be able to train with the same volume during cutting. Assuming classing cutting of ~500 cal/day from surplus of ~500 cal/day, we are looking at ~1000 cal/day different in energy consumption. Assuming you are not planning to be at the gym for 4 hours - I highly doubt that same volume can be achieved (or should be achieved, for that matter). While cutting, the main goal is to retain the most amount of muscle mass, so decreasing volume from the bulking levels is ok. You probably will lose some muscle mass, but that is a part of the deal, when you are cutting.
As to cardio, I prefer HIIT, but doing it every day is unmanageable, and according to some literature, down right bad for your heart. You can do cardio every day, but alternate between steady cardio and HIIT. If you only have time for cardio 3 times a week because the rest is taken by lifting - just do HIIT.
- 5 min warm
- 10-15(or even 20 if you are THAT good) HIIT,
5 min cool down.
I wouldn't add much lifting after HIIT, simply because it is a very energy-depleting process. If you try to lift something heavy afterwards - your form may suffer and/or you may get an injury.
If you have a recovery day, and you still want to do something, recovery 1h walks with some incline may be beneficial.
As to progressive overload.... Within the cutting face, you will probably need to drop some weights on your working sets ( eventually ). That is ok. If you really feel that you can progress, increase the intensity.
- Shorten down the break time.
- Add extra couple of reps.
- Do an extra set, if you must.
The goal here is major decrease in body fat percentage, so don't run after strength progression, just try to lose fat without loosing too much muscle.
And the best advice you can have and I can give: educate yourself... A LOT!!!
Read a crap load of articles, a book or two, talk to someone who you think is a knowledgeable person in what you are trying to achieve.