Joe, in NJ the standard contract specifically does not allow assigning of the right to purchase (without Seller's consent). 

The paperwork also says that consent cannot be unreasonably withheld but I'm not sure the reason I have for wanting to move is an acceptable reason.

This violates the lease because it states no repair/changes are to be done to the property without the consent of the landlord.

There have been reports of physical fighting going on in their garage and in their unit, but all the tenants of that unit "consent" to it, according to the records, so there's no "abuse" technically. 

OCCUPANCY: Only those persons whose names appear on the Lease may occupy the Rental Unit without our prior written consent.

My biggest concern is primarily bogus esa rules where tenants can get a dr note saying they need a pet or pets and then having one for free without my consent especially if it is a restricted breed I can’t insure.  

Don’t try to do it with out the owners consent.

(there was a tax lien and a cancellation on that lien filed back in 2015) Is there a way to figure out if the existing mortgage was ever satisfied or what the current balance is without getting written consent? 

My husband specifically put in the lease that no additional people could move in without consent.

And they can charge $250 repair and maintenance without consent from owner.