I see what you are trying to accomplish but I think you are mixing apples and oranges. The reason for rest in-between sets is to restore depleted ATP so that the next set can be performed. Depending on the load when lifting weights, it will take a body so much time to accomplish this, and it is not heart rate dependent.
In aerobic interval training, you cycle between intervals of higher and lower intensity in whatever parameter you choose with the goal to achieve greater aerobic fitness and also to expend more energy. Using heart rate or RPE is an appropriate parameter here.
There are of course all kinds of hybrids such as peripheral heart action system and any variety of super-sets but even those operate on depletion of ATP with the goal of increasing strength endurance.
I am curious to see how my colleagues will advise.