Fin roles generally require relevant points in profile that you can build during your college life.
There's nothing as such core mba role, what you might be referring to is a general management role, which prefers people with workex.
Regarding the part to get away from IT, you'll get the best opportunities in IT sector given the pre-mba workex. So will suggest not to be so adamant on avoiding IT space.
Your current pay sounds good, if there's no other constraints & confidence on getting better score, one more attempt sounds just okay.