I thought I would add a line in their lease extension, due in December, that it could be assigned in the future.

You should first look at what your lease says for repairs. 

I mean this in the sense that if someone called it goes to auto answer with a telepromt that says press 1 for maintenance, 2 for lease and rent and etc... this way the tenant is able to make their voice and problem heard but i don't have to sit and have small talk and constantly stop what im doing to answer a phone call that in all reality shouldn't have been made.

However, the part of rent control that pertains to asking them to move out when the lease is over still applies.

I have a tenant that ended the lease w/ 4 months left.

The only issue would be if the military member accepted a transfer that also meant the family was going with them and there was still some lease left.

Currently they are paying $700/month but houses on the same street are paying $900-950/month, so I was thinking about raising rents once their current lease expires.

If their previous lease was month-to-month, you can do this easily and quickly.

I have long term (inherited....) tenants that currently live in my other unit with their lease set to expire in June of 2019.

The other good reason to have a Real estate license is if you are a Property Manager and lease units you also may be entitled to extra compensation while collecting a paycheck (for now) and gaining experience.