In Genesis 1:26, there aren't in fact three instances of "us". There is only one instance, "We will make", or "Let us make", followed by two possessives of the same number. The verse can be translated equally well as "Let us make mankind in our image and likeness" - with only two "us"s, as the Cambridge "New English Bible" translates. Furthermore, you might notice a glaring change of number in this verse as "mankind" (Adam) is first referred to, apparently, in the singular, and then in the plural when ruling the fishes of the sea and the fowl of the air, and then switching back to the singular again on the following verse when God creates "the man" (ha Adam) using only the first trait, the "image" (what happened to the "likeness"?). So we are on shifting sands if we try to build working religious doctrine based on translations of our ancestors' rather fluid view of grammar.
Regarding the usage itself, there are other examples, such as:
In II Samuel 24:14 David says to Gad "... Let us fall into the hands of the Lord..."
In II Samuel 16:20 Avshalom says to Ahitophel "Give us your advice, how shall we act?"
In Exodus 1:10 Pharaoh suggests "Let us trick him lest he increase and when war breaks out he will join our enemies and will escape from the land."
In each of these cases, as in Genesis 1:26, an individual uses the plural (we or us) when considering some action, even if he is the only one deciding or taking the action. In English we might think to ourselves "Let's say the butler did it", or "Let's go surfin'", even when we are one person going to the beach alone, because in English, as in Hebrew, that is the way we express a hypothesis or a proposal pending decision. And in light of the consequences of this particular decision, it was indeed wise to consider carefully, certainly worth the extra verse (which thematically ties into Genesis 6:6 and Genesis 9:9-18).
The context of Genesis 1 uses singular voice consistently when referring to God. Both texts of the Decalogue and Deuteronomy 6:4 leave no doubt as to the final interpretation.
Note that this answer does not answer the OP as does this answer; rather it questions the premise of the OP.