I think it depends also on your body type.
I happen to be tall and slender, and have a high gas exchange ability. Consequently when swimming slow my muscles stay in aerobic mode for a long time. This results in me having to end to dive because of low O2 for the brain, while my muscles have hardly any lactic acid build up. To counter this, I came up with the following approach for my maximum dynamic dives. First 50m I swim compact, slow and as relaxed as possible. When the contraction start I 'step on the gas', speed up to 75% - 80% speed, trying to relax the chest, head, while having my legs and abdominal muscles work in anaerobic mode. This way I think I avoid my muscles using the O2 in my blood, leaving that for my head, while using the anaerobic capacity.
I've tested this approach in both apnea walks as well as for dynamic with monofin, yielding in two nice pb's. (+25% / + 12% resp.)
I agree with Simon on the part that one should try to remain as relaxed as possible, the only distinction I would like to add is that this applies in my view mostly for the mind and body parts not used for swimming. Swimming a bit faster can be nice liberating transition to the second part of the dive. Make sure it stays a compact and efficient swim stroke though. I use the turns as places to relax and rest.
I'm interested to hear your experiences with my dual speed approach.
Love, Courage and Water,
Kars