It's not that simple, for a couple of reasons.
The difficult reason is that there's a tempting and tantalizing possibility. You see, a half Knight when augmented becomes as strong (roughly as strong) as a FIDE Knight; and a Halfling Bishop, when augmented, becomes roughly as strong as a FIDE Bishop; and so wouldn't it be wonderful if one could make the augmented halfling R and halfling Q just as strong as their FIDE counterparts? Wouldn't it just be a spiffy game if one could do that? It is sad, but I think it cannot be done, and have spent days on the problem.
The easy difficulty is that the Crab, which is the Half Chess Knight is itself one of the Augmenters; also the alternate Knight from Augmented Chess is the Fibnif, and the Half-Fibnif, which would be ffNbF, is an untested piece (and not a pretty piece like the Crab).
The Narrow Half-Knight is an augmenter, but it could be easily used as a basic piece, to which W or F might be added as Augmenters -- you would not want to add the D or the A because the augmented piece would be able to visit only half the squares on the board -- but adding the F to the Narrow Half-Knight gives you the Fibnif!
If you can have the Fibnif as an augmented half Knight, why can't you have the Knight? Artistically, the Knight has to be there; and so the simplest way is to allow the Wide Half-Knight as one of the augmenters.
And so the difficulty is resolved: the two alternate Knights must be the Crab and the Narrow Half-Knight, and the Augmenter list includes the Crab, the Narrow Half-Knight, and the Wide Half-Knight, and an additional rule is added so that you cannot choose the same thing to be both a basic piece and an Augmenter. (We can pretend that this rule was already there in Augmented Chess, because in that game none of the basic pieces were also Augmenters.)
Now the rules can be written.
The first special rule is that when a Pawn promotes it may promote to any piece that was in the game at the beginning.
The second special rule is that when choosing pieces no augmenter should be used twice by the same player, and a piece that is chosen as a basic piece may not also be used as an augmenter by the same player; that is, if you have chosen Halfling Rook plus Ferz as your Rook, you may not choose Crab plus Ferz as your Knight.
Notice that it is permitted to choose the Crab as your basic Knight and also to choose the "Halfling Rook plus Crab" as your basic Queen.
The above are the rules. Specific discussion of the basic pieces and the augmenters will follow, after some general observations about the game.
Some augmenters cannot reasonably be chosen with some basic pieces, for example you cannot choose Halfling Rook plus Wazir, because that is the same as making no choice at all. hhRook plus Dabaaba is not completely worthless, but it is clearly a weak choice. hhBishop plus Dabaaba is a slightly weak choice because it is assumed that the Bishop would gain more from being able to move to squares of a different color, with hhBishop plus Wazir, or hhBishop plus Crab, or hhBishop plus Narrow Half-Knight.
It is possible for both players to select the same army, though it may be unlikely. More likely, both players might have (for example) the same Knight but different Rooks; there is an obvious set of alternate rules of the game which would forbid two players to use the same piece, but that makes the rules more complex and so I decided to allow it.
W: The Wazir moves like a Rook, but only one square.
As an augmenter, the W adds more mobility to the combined piece than any other augmenter does. This strength is balanced by its lack of range and its awkwardness in blocked positions.
F: The Ferz moves like a Bishop, but only one square.
The F is second in added mobility, and its diagonal move is flexible, and the fact that two of its moves are forwards is good; however, it is short and does not shine in blocked positions.
D: The Dabaaba jumps two squares in the direction a Rook would move. It can leap over obstacles.
As an augmenter, the D provides quick development plus some ability to sneak past Pawn chains or to deliver a smothered mate.
A: The Alfil leaps two squares diagonally, over obstacles as needed.
As an augmenter, the D provides quick development plus excellent ability to sneak past Pawn chains in blocked positions. It can deliver a somethered mate, and because it has two forward moves it has better forking power than the D.
Crab: the Crab moves to half the squares a Knight can go to; forwards narrow and rearwards wide.
As an augmenter, it has the advantages of a Knight; but of course it goes to only half the squares a Knight can go to, which keeps it from being too powerful.
Narrow Half-Knight: the fbN moves to half the squares a Knight can, narrowly forward and narrowly to the rear. For example, from e4 it can go to d6 or f6 or f2 or d2, but not to c3 or c5 or g3 or g5.
The fbN is not very different from the Crab, as an Augmenter. As a piece by itself, of course, it isn't very good because it can't see most of the board.
Wide Half-Knight: the shN moves to half the squares a Knight can, but only the widest ones. For example, from e4 it can go to c3 or c5 or g3 or g5, but not to d6 or f6 or f2 or d2.
The Narrow Half-Knight is not a good piece until it is augmented; the reason is that by itself it can only visit one fourth of all the squares on the board. When you add the Wazir or the Ferz or the Wide Half-Knight to it, you get a Knight of full value.
The Wide Half-Knight is provided mostly so that you can add it to the Narrow Half-Knight and get a regular FIDE Knight.
The Chancellor is Rook plus Knight, just as the Queen is Rook plus Bishop. There are two kinds of Half-Chancellor, the Halfling Rook + Crab, and the hhR + Narrow Half-Knight.
The five types of Augmented Half Rook are hhRF, hhRA, the two half-Chancellors, and the Halfling Rook plus Wide Half-Knight. Choosing a half-Chancellor as your basic Queen-type piece and then making a half-Chancellor by augmenting your Halfling Rook seems to violate the spirit of the restriction about using the same thing twice, but the rule is written in a way that allows this because otherwise the choices become too restricted.
There are five types of Augmented Half Bishop: hhBD, hhBW, hhBffNsbN, hhBfbN, and hhBshN. Because the hhBD is still colorbound, it is expected to be an inferior choice. Augmented Half-Bishops are stronger than Augmented Half Knights.
Every type of Augmented Half Queen uses some sort of Knight power. Your choices would be severely restricted if the restriction about using the same piece twice forbade you from using the Crab as your basic Knight and the hhR + Crab as your basic Queen. In fact, the rule was not written that way, and so the same power can appear twice in this one circumstance.
It is interesting to see how things come out when you mix the rules of Half Chess with those of Augmented Chess. What makes it interesting is that the basic pieces of one game are augmenters in the other game -- well, at least some of them are -- and this causes a conflict in the merged game, although it also provides some of the interest of the merged game.