You have interpreted the meaning of intensity correctly, but just to be clear I am not advocation solely exercises in the 1-3 rep range. I am simply suggesting that as you feel that you are losing energy in the gym due to caloric restriction that you shift moderately to a higher intensity from higher volume. Throwing in a 1-3 rep set every now and then is fine or even doing like 8 singles to change things up a bit is cool. Still, you don't want to reduce your muscles time under tension too much. I would suggest maybe the 6-8 rep range in general playing around with your lifting tempo to make sure you are giving your body sufficient stimulus.
It is true that a caloric surplus will not permit you to lose weight or fat. However, it sounds like you have used your bulk as an excuse to eat unhealthful calorie rich foods. The advantage of eating lots of protein, healthy fats, and limited but strategically timed carbohydrates, is that you will find that your body will tend to put on more LBM rather than fat. Of course it is difficult to eliminate fat gain entirely.
I still think you need to look in the mirror and decide if you have reached the level of muscular development to warrant cutting lest you never realize your potential to put on muscle mass. At 180 lbs and 5'9'' I doubt this is the case.
Also, if you start cutting to say sub 10% bf you will weigh something like 160 if you lose no muscle at all. Since this is not likely to be the case, my guess is you would weigh 150-155 if not less. Is that really your goal? Do you really lift weights so you can look like a muscular adolescent? My guess is that if you reach your dieting goals you will have another bulk in your future.
My advice is to get strong and big and not be unduly concerned with bf percentages. On a bigger more muscular frame you will likely carry your bf better anyway. Good luck with whatever you decide.