I think you will find the meaning of the words or even have found it out already, so i will not explain it, and start analyzing the two opposite sentences السلام عليكم أيها النبي and السلام عليك أيها النبي from a fiqh and a linguistic POV.
Saying السلام عليكم أيها النبي in tashahud?
The (plural) version you wrote down here السلام عليكم أيها النبي is unknown to me and as you mentioned it sounds wrong and even a search on Sunna.com shows that this version is not quoted in any (major) hadith collection.
Maybe it's a printing error or a special case for a special madhab as the well known and good referenced version is the singular form السلام عليك أيها النبي you may find evidences for an other version السلام على النبي for example in Muwatta' Malik. These both versions are acceptable both in Arabic language and at situation of the tashahud in prayer.
About your shirk matter:
We know that often we use the plural form السلام عليكم even if we greet one person this is also according to the rules of the Arabic language acceptable, as in cases the singular can be replaced by the plural and vice versa and we have many examples of this in the Quran you may find it out if you read the Quran in different riwayat for example surat al Kahf (20) in some riwaya it's the wind/storm= الريح in others the winds = الرياح and even in the story of the two man among one was apparently a believer and the other a rich man who had to gardens some riwayat seem to forget that the man had two of them and go ahead considering one garden others go ahead speaking in the dual plural form!
Now about the matter you addressed السلام عليكم seems wrong as we are addressing our Messenger (may peace be upon him) as a single person! I think i have to possible explanations:
- The plural form is a kind of way to honor him as in Arabic the equivalent a way of the honorific speech is using a plural انتم (examples: سيادتكم, فخامتكم) so you use this might be a reason for that.
- An other reason might be as we do the salat 'ala an-Nabiy الصلاة على النبي we often include his family or even his sahaba in it so a plural form would be acceptable.
And finally in this case shirk isn't a matter as yes we believe in one God, but it's not him who is addressed by these words. On the other Hand assuming the plural form is correct i think i have given evidences that it could be considered either to honor or to add Ahl-al-Bait (May ALlah be pleased with them) into the tashahud which is totally acceptable because of the salat al ibrahimya (for example, which is a part of the tashahud and addresses both Aal-Ibrahim and Aal-Mohammad (May peace be upon both of them)): so shirk seems out of question, unless your intention was something different!
And Allah knows best.