To answer your question, it seems that there is a grammatical necessity for Paul using κοινωνος in some verses and κοινωνια in others.
First of all, note that the masculine form is used when actual participants/partakers are being mentioned. As you are probably already aware, many languages (including Greek) use something called the "masculine universal." This means, to put it simply, that αγιοι (masc.) can be used to refer to holy ones, even if some of them are female. Alternatively, one could use αγιοι και αγιαι (meaning "holy men and holy women"). But it would be grammatically inaccurate to use αγιαι to refer to a group of holy ones if the group includes men.
Secondly, κοινωνος refers to actual participants whereas κοινωνια refers more to the participation/group itself. This was my conclusion after examining all the NT uses of each noun and from what HELPS Word-studies says on the matter.
[2842 /koinōnía (a feminine noun) stresses the relational aspect of the fellowship. 2844 /koinōnós (a masculine noun) more directly focuses on the participant himself (herself).
Significance (of course, speculative!)
Nevertheless, we must keep in mind that Paul could have written his sentences with a different structure. If he wanted to use κοινωνος in 1 Corinthians 10:16, he could have written, "By blessing the cup of blessings, are we not participants (κοινωνος) in the blood of Christ?" But Paul didn't do this!
Notice that in 1 Corinthians, each use of κοινωνια refers to the Christian community. (In fact, all uses of the feminine form in the NT have positive connotations.) Contrast this to both uses of κοινωνος. κοινωνος is used only two verses later in 10:18 to refer to those who still follow the Mosaic Law with its animal sacrifices, and is used again in 10:20 to refer to pagans who sacrifice to demons.
Could it be that Paul (or perhaps the Holy Ghost writing through him) deliberately structured his sentences to parallel following-the-Mosaic-Law-after-the-veil-was-torn with pagan devil worship, setting both aside as evil and opposed to Christianity? Or was this just a coincidence? If the Book is divinely inspired by a God of infinite intelligence, can there be any coincidences? I'm still "on the fence" whether or not it is a coincidence.