Well the "works best" for Alpha is more like 154* to 162*. And I don't think sitting at a temp for 5 minutes is enough to really convert anything, you have to be there at least 20 minutes, so that would be why people looking for Beta don't jump ahead to get the Alpha first.
If you can step up the temperature (using direct heat or heated additional liquor from the HLT) I would suggest you mash for 45 minutes at 140*, then 20-30 minutes at 153*. Get all of the Beta out that you can, then a rest at the low end for Alpha to get that additional body.
The easier way for what you're looking for - mash for 45-50 minutes at 145*, then do a mash out. You'll still get some Alpha, but you are really in the wheel house of the Beta and will be highly fermentable.
And a side note - you also have a problem if you were stepping down in temperature, that you would want a mash tun to quickly get rid of heat. but you want these designed to hold heat well. Also, you then have colder wort in the mash that now needs to have more work done to raise the temp to mash out, then out to boil kettle to 212*. Its a shorter brew day if you are working towards the eventual goal of 212*.