In order to get a Post -graduation degree from Philosophy, the idea of persuing CCS university is not bad. You can do your Post- graduation in private as well but for this, you need to seek permission from the Vice- chancellor for the continuation of the same.
Yes, a migration- certificate is required in the event of approaching a new university for continuation of a course and in your case, the same thing would apply.
My line of thinking is somewhat different. You could have seriously considered doing a doctorate degree in Mathematics from Gurukul Kangri University and afterwards you could join as a lecturer in some private college and later by clearing the NET test, you could get a permanent post of Lecturership in a Government - college.