I am unsure if the crime faction stuff is among the "baked-in" things that can only be solved by a New Game, or if it can be retroactively removed. IIRC, baked in stuff that can only be solved with a new game with USKP. It doesn't say anything to that effect, so it's probable that it'll be okay.
Also, it is imperative that you get the Unofficial Patch for all the DLC. You can't just use one, they are designed to overlap each other. For example, Dragonborn DLC alters the dragon absorb scripts. The USKP cleans it up and also fixes the "no absorb dracs at word walls you already visited" bug, but if Dragonborn DLC is also loaded but without the Unofficial Dragonborn Patch, dragon souls won't absorb at *ALL*. UDBP amalgamates the Dragonborn DLC changes with the USKP fixes.
This may change with the planned (but not yet implemented or officially released) change to make all the Unofficial Patch modules into quasi-ESMs to load amongst all the other true ESMs, though.