WoW!
That is one hell of an answer.
Thank you bbkfp for the whole bunch of information.
I do have some questions,
A) Why are you not migrating Archived data? I do want that data.
B) With your step 5 '5.) delete redundant profiles, update autoincrement and run core:archive', you deleting redundant data, exactly what type of data will be redundant even after changing the both of the idSite's to '1' (taking your example). Coz, I cannot dare to loose any data and to scroll through my whole dataset to find out which data will be redundant is not an option as I have very huge collection 
C) What exactly are you doing here? archiving all the data under idsite = 1 in new Piwik (piwik_3)?? can you shed some more light on this.
d:\inetpub\piwik_3>php.exe .\console core:archive --url=https://piwik.example.com/piwik_3/ --force-idsites=1
I am new to piwik and trying different things with this,
Thank you for your terrific answer.
I would really appreciate your help at this, http://forum.piwik.org/read.php?2,130323, I am stuck at this point for very long and unable to find a solution for it.