I am by no means qualified to speak on pool technique, but I really think there is no such thing as a sinker. As someone else mentioned, a lot of people START to sink. If they waited a second, they'd reach neutral bouyancy or better and start to at least hover, but then they exhale or start to get vertical and sink.
The biggest variable in body bouyancy is body fat. Unless you are marathon runner lean, you aren't negatively buoyant. The difference between 10% and 15% isn't going to make one guy float and the other sink.
Stick with it and use the tips above and you'll be fine.
The biggest contributor to success in survival swimming is confidence in the water. Once you panic or start flailing, you're done. Nothing in survival swimming has to be done quickly. As long as you approach everything in a calm and methodical manner, you'll be fine.
I never liked the SWET trainer. At first, I would always be out of the seat in 2 seconds, then barrel through the cage like a bull in a ring. Once I realized that, hey, I can hold my breath for a minute and calmed down, things were much easier.
Body builders tend to sink too, muscle weighs more than fat.
It's easy to say don't flail but if you're uncomfortable in water it is a natural reaction. The key is to come to grips with it as soon as possible and try to relax.