Again this is an interval session so as a reminder:
Interval runs are designed to increase your oxygen supply and your ability to use that supply. If you manage to increase both, then you increase energy production, and you go faster - Simples!
However, you don't increase your oxygen supply by breathing in more air. You increase it by improving the transportation of oxygen to your muscle fibres.
If you don't improve the transportation of oxygen around your muscle fibres taking in more air is like putting 50 litres of petrol into a 25 litre tank. Lots of spillage but no more available fuel!
It takes about 2 mins to reach your VO2Max from a resting pace. For the workout to be effective, you'll need to run repetitions at a minimum of 90% of your VO2 Max. So it's important that whilst you recover between reps, you still don't let your heart rate drop to much so that it quickly return to 90% of your VO2 Max and you spend more time in this zone.
If you run slower is wont stimulate the improvement you are after; if you run faster, it will leave you more fatigued without offering any increase in benefit relative to the purpose of the workout.
Good luck and enjoy!