You're right about the vicious circle.
What do you think of taking back, maybe, half the city's park property, selling it to private ownership, thereby getting it on propert-tax rolls?
Sadly, it seems: (a) Anchorage lacks a mayor-Assembly form of government with the character which New York officials showed in reducing NYC's crime rate to manageable levels (b) the fact that residents have to beg for law enforcement suggests city officials may intend to hold the issue of public safety hostage so as to force a sales tax, and (c) nothing will change until the city's mail-in voting system is scrapped and traditional polling places are restored.