Hi Barney, welcome to DB!
I hope you've got a close and dedicated buddy, and you do not push your boundaries doing those exhale statics; because a BO comes very sudden when doing exhale dives, and you're a long way from the surface.
Ok, 2 reasons why your contractions start so early; 1 the air in your lungs becomes faster saturated with CO2, secondly the physical chest and diaphragm deformation due to pressure induces the feeling of being crushed/suffocation.
In all honesty I must say that I think doing empty statics at the pool bottom is not effective. Exhale dives can be used to learn to equalise; though you'll need instruction and close supervision to do that.
Let's offer you some alternative. The Crazy table. You need a buddy, and a shallow pool. The goal is to get used to a sustained lower O2 level. It for sure will also be very CO2 demanding, and it's an advanced technique only to be done with a very able freediving buddy(!).
How: Exhale your air and hold, close to the wall on which you gently hold on with your hands - not sinking deep(!). When you need air, come up a litle and take 1 sip of air IN and continue your hold. Repeat sipping air in until you're lungs are full.
This is a very demanding session.
Off cause a steep CO2 table is also good practice; Something like 2' - 2' hold - 1'30 pause -2'h -1' pause-2'h-0'30 pause-2'- 1breath/15sec pause - 2'h -1breath/15sec pause - 2'h -1breath/15sec pause- 2'h -1breath/15sec pause - 2'h - etc.
I've a personal best (pb) of 7' and use these, and find them very challenging, as well as exhausting, So I strongly advice you to go slow and feel your way carefully because it's easy to over train in freediving.
If you do not have a good buddy (I repeat my self often because it IS so IMPORTANT), do only the dry breath-holds.
Finally, if you consider yourself a true beginner, pb < 4 minutes, then you'll find that the most performance gains are to be had in flexibility, relaxation, meditation, preparation. In other words focus on learning an enjoying your mind and bodies movements, leave the timing up to your buddy. If you really want to learn fast; do not record time at all, for it's such a strong energy consuming distraction.
If you have not done any Freediving course; save up, and go there fast; you'll learn months of trial and error in just a few days plus you'll get to know our lovely peer freedivers, and beautiful people they are.
Be careful and have fun.