Beta is responsible for conversion. Beta converts glucose (non reducing end) into maltose, the sugar that helps beer to be beer. Enzymes don't really convert starch into anything.
I am curious as to where you got some of the ideas you put in this post. I chose this one as an example as it was the one that hit me in the eye like a wet flounder.
Beta does not convert glucose to maltose and if it did it would use both the reducing end of one glucose and the non reducing end of the other (maltose is a-D-glucopyranosyl-(1-->4)-D-glucopyranose in which the 1 carbon is the reducing carbon and the 4 the non reducing carbon on the other molecule). BTW, 'reducing' here refers to the ability of this end of the sugar molecule to reduce Fehling's solution (a blue Cu(II) complex) to red Cu(I) oxide.
The reactions in the mash tun are extremely complex and still not completely understood (certainly not by me at any rate). A simplified explanation of what happens in essence follows.
The two prevalent types of starch found in barley malt are shown in the sketch. ß-amylase chops off small bits from the non reducing ends (represented by solid hexagons and the singe reducing end, which is at about 4:30 just inside the dashed line, in the amylopectectin part by an asterisk) of both types. As it prefers the penultimate 1-->4 bond at a non reducing end maltose is the sugar produced in greatest proportion. When attacking an amylopectins it can only munch down to within a couple of sugars of a 1-->6 branch points (leaving all the reducing ends within 2 or 3 units of a branch). The result, absent other enzymes, would be a 'limit dextrine' shown by the dashed line in the sketch. Now a-amylase (there are actually 3 of these) can break the 1-->6 bonds allowing ß to continue its march towards the reducing ends resulting in more maltose than there would be if the 1--> 6 bonds were not removed.
This is the executive summary. There is more to it than just this. Other enzymes are involved and other sugars are produced. Each enzyme is effected by temperature (both in terms of reaction kinetics and the length of time it takes to denature it at a given temperature). Brewing practice is determined more by determination of what works best than by activity studies of different enzymes though, of course, those studies lend insight as to what is most likely to work well.
Anyone who wants to understand this better needs to consult a text such as Brewing Science and Practice (Briggs, Boulton, Brookes and Stevens) (from which I got the picture).
As the real goal here is to improve body the followings steps should be taken:
1. Make sure there is enough chloride in the brewing liquor
2. Use a hefty amount of malt (shoot for OG of 12 - 13 °P)
3. Don't rest too long at the protein rest temp (leaving the rest mash at the protein rest temp for as long as it takes takes to process a decoction shouldn't be a problem - at least never has been for me). If you get good head you should have plenty of body.
4. Saccharify at a higher temp (150 °F).