Beta amylase can only chop maltose from what's known as the "reducing end" of a poly-glucose chain. It can completely convert the amylose form of starch since there are no branches. Amylopectin has branches in the chains, so beta can only work from a reducing end up to the branch point (actually a few glucose units before the branch), and then it gets stuck. The chains past the branches would never get converted. So, you cannot convert all available starch with just beta amylase.
Alpha amylase can chop up the poly-glucose chains at random points, resulting in random size glucose chains. Alpha can also not break the chains near a branch point, but can attack the chains from either end, and between branches if there are enough glucose units between branches. You need at least a little alpha amylase action to get a fully fermentable wort (just maltose, glucose, and limit dextrins.) Alpha amylase will work at temperatures within the optimal temp range for beta amylase, but the action is much slower. Also, alpha amylase is not as efficient as beta at creating the fermentable, small molecule sugars.
Once you have cut up the long chains, you can't put them back together to get a less fermentable wort. Fermentability only increases with increasing time (increasing enzyme action), and chain length continuously shortens. What you get at different temperatures is different rates of action for the two enzymes, and at higher mash temps the beta amylase gets denatured faster, so that most of the action comes from alpha amylase. If you want some residual longer chains, just mash at higher temps, but not for too long. Or, put in some malt that can't be converted as well by the amylase, like dextrin malt, crystal malt, or roasted malt.
Brew on