Fats are calorically dense food that don't trigger insulin release.
As you appear to have found out, you want to consume low glycemic index foods that don't trigger insulin release.
Food of Color
An easy rule for insuring you select low glycemic index vegetables is to chose those of color. As an example, green beans over a Russet potato.
Milk is an interesting food.
It has a low glycemic index rating.
However, milk has a high...
Milk/milk products are insulinotropic, trigger insulin release.
Inconsistency between glycemic and insulinemic responses to regular and fermented milk products
"Despite low glycemic indexes of 15?30, all of the milk products produced high insulinemic indexes of 90?98, which were not significantly different from the insulinemic index of the reference bread."
This amino acid triggers an insulin response.
Thus, proteins high in Leucine need to be monitored in your diet.
Whey protein appears to have the highest percentage of Leucine, 10-12%.
With that said, let me provide this...
Health normal individuals should gravitate to milk and Leucine rich proteins post workout.
1) Insulin is a very anabolic peptide hormone.
2) Leucine has been shown to trip the anabolic trigger, mTOR (Mammalian Target of Rapamycin)
Sprint interval running increases insulin sensitivity in young healthy subjects.
Sprint interval running increases insul... [Arch Physiol Biochem. 2012] - PubMed - NCBI
Sprint interval have been shown to increased insulin sensitivity.
Thus, "Sprint" Training type program should improve you condition.
"Interval Sprints" For Muscle Mass
Interval sprints have a bodybuilding component to them.
A 10-30 second sprint, short rest, then repeat.
Hypertrophy "Bodybuilding" Training
Weight training for hypertrophy applies the same principle.
A short "sprint" of 8-12 reps in an exercise.
A short rest period, 30 -60 seconds, the repeat.
Cardio with Drs. Norton and Wilson (Audio Seminar)
Muscle College with Dr. Layne Norton & Dr. Jake Wilson! The Doctors talks CARDIO!!!
This audio examines how sprint increase muscle mass.
1) Cycling is mechanically similar to Squatting or Leg Pressing. (at the32:45 minutes mark)
2) Ultrasound measurements of the muscle during sprint interval cardio established an increase in muscle size. (at 51:00 minute mark)
3) Swelling of the muscle (The Pump) creates growth. The swelling of the muscles from Interval Training is huge! (54 minute mark)
Intervals = Hypertrophy
The take home message is that you can improve you insulin sensitivity and increase muscle mass by employing Interval/Bodybuilding Methods.
This type of training has also been show to increase protein synthesis, increasing muscle mass.