mashing at 145 - 158, slowly heating up

What would happen if you started your mash as say 145F and slowly heated the mash, so that after 20 minutes it was 151, and than after another 20 minutes it reached 158?

This would give the Beta Amylase 15-20 minutes at its optimal temperature,
and the Alpha Amylase 15 minutes at its optimal temperature.

I don't think this would yield 2 opposite beers - both thin/dry and sweet (and thick).
How would this work out?
Has anyone done this, and how did you like it?

Well the theory is that most of the conversion happens within the first 10 minutes of the mash so I would think that you would end up with a thin/dry beer that is not at all sweet.

I think a better approach would be not to let it rest at 145 but to slowly heat it immediately from 145 to your target high-temp, 158 in this case, but to hit that temp within 20 minutes as much of conversion happens at that point.

You can do that but the temp ramp needs to be slow and you have to mash for an extended period of time. What you are talking about doing is basically the same mash process as Bud Light.

If you raise the temp too fast you are going to denature the enzymes and basically get awful efficiency. You need both enzymes working together to get the mash to convert properly. Beta may like it cooler than Alpha but if Alpha is not working to break down long chains then Beta has nothing to do in the first place.