Is reenlisting the best and smoothest path to change your MOS?

Well to be a 36B the MOS has to be open when you request reclassification towards the end of your contract also you need to be in an MOS that has an Out call as well meaning they’ll allow you to leave your MOS to another

Reenlisting gives you some leverage as long as the Army is in need of Soldiers. From now until you're within your reenlistment window, stay out of trouble and do your assigned job to the best of your ability. If time and money permits, look to better yourself by taking college courses. Make sure that you meet the requirements of a 36B. As SSG Johnson mentioned, in order for the reclass to happen without jumping through hoops, the Army has to have a need (IN) of 36B's and an overstaffing/at staffing (OUT) of 92A's. The Army is about give and take. Let your name be known throughout your company and battalion by the good that you do. This would put you in a better stance where your leadership are more willing to help you.

Sorry, there will most likely never be an open class seat for 36B and their MOS is always full. It is a very tiny MOS which leads to slow promotions.
You do not need to be in your reenlistment window to reclass. You must have one year on station, not be on assignment, your MOS must be balanced or over strength and you must request a more under strength MOS than yours. Most importantly, there must be an open class seat.