Your answer will probably revolve more around the amount of experience you have versus the amount of equipment. Those low volume/high intensity programs tend to work better for advanced trainers who already have maxed out their genetic ceiling when it comes to work capacity.
The reason why is the first 5 to 10 years the majority of people will find their greatest adaptations lie in the accumulation of volume (when it comes to bodybuilding the same can be said for increasing the amount of weight on the bar). After that time your ability to do more pays off less (in the form of stalled progress and injuries) and then gains tend to rely more on your ability to generate higher levels of intensity. Granted none of this is absolute and varies depending upon the person you are talking about but as a general rule it tends to stand up very well for most of the population.
If you look at guys who had a lot of success owed to HIT techniques you will find they came from a more traditional lifting background. Mike Mentzer started out being trained by powerlifters and olympic lifters and had fairly elite levels of strength in exercises like the squat, clean and jerk and bench press (at a very young age no less) before he ever got into HIT and Nautilus equipment. Same for Casey Viator, Sergio Olivia and Yates.
You can do an awful lot with just the equipment that you listed because HIT really comes down to the amount of internal tension you can place into a muscle. Arthur Jones used to call these "inroads". The limiting factor with such systems is very few young/inexperienced trainees have the motor unit recruitment ability to get very much out of training that way and even then a good 20% still responds better to higher volumes instead. The remaining majority (80%) falling somewhere in between the volume bell curve.
Please note I am not a mathematician so those percentages are really just something I pulled out of my ass based on my personal experience as well as being around gyms and being a trainer for over 20 years.
Best of luck.
(Please note the image of Viator is from Zack Even Esh's site)