The short answer is, forget sprints, sled pulls and all that. Buy a heat rate monitor and do something that keeps your heart rate between 140-150 for between 30-60 mins 2-5 times per week. Whether that be light jogging, walking uphill on a treadmill, cycling... whatever.
The long answer... The body has three energy systems:
The anaerobic alactic - very intense effort - lasts 10s or less
The anaerobic lactic - intense effort - lasts 90s or less
Aerobic - moderate effort - lasts hours
Powerlifing and most powerlifting training is pretty much 100% alactic and the processes of recovery between sets in the gym and lifts at a meet are pretty much 100% aerobic. The lactic energy system isn't much use to a powerlifter.
What is important for a powerlifter is the heart's stroke volume (the amount of blood it can pump per beat). Increased stroke volume means the heart can move more blood around the body with less effort; supplying more oxygen to the muscles, clearing out the metabolic byproducts of the anaerobic energy systems and 'refueling' the muscles faster and more effectively between sets/lifts.
But, sprint intervals, sled dragging etc. mainly target the lactic energy system (intense effort for bursts of 90s or less). They do also train some aspects of the aerobic system, but not the most important (the heart's stroke volume) and at a high cost in terms of fatigue.
They don't effectively increase the heart's stroke volume because above heart rates of about 150 the heart doesn't get time to fully fill with blood each beat and 10-20 mins isn't long enough to effectively train stroke volume. They can also increase the thickness of the walls of the heart, which can actually reduce stroke volume. Lifting weights does this too.
Stroke volume is only effectively increased by low intensity steady state training for over 30 mins at heart rates of under 150. This basically stretches the heart as it is filled to it's full capacity each beat constantly for 30 mins+.
So, I think easy steady state training is all a powerlifter really needs in terms of cardio. I've seen massive benefits in terms of my work capacity in the gym, and feel generally much healthier, since I jumped off the intervals bandwagon and started doing easy steady state training on my off days.