I'd spray it (no brushes) or rip it out and redo it with new MDF trim pre primed.  

The management has sprayed/bombed/fogged every other day for a week.

You'd probably learn a bit about electric work also.I've been fortunate not to have too major catastrophes with tenants.I had a roach infestation which was like something out of a horror movie.Tenants removing doors, spray painting graffiti on cupboards and doing severe wear and tear.

  $425 to spray treat and bait termites.

You also have to pay fairly well to keep competent employees that are willing to work on a hot roof all summer in 100 degree Central Valley heat spraying foam in tyvek suits and respirators.

After driving through the back alley, the back unit has been tagged and needs a paint job, as well as security lighting and maybe a spray-paint-resistant coating?

or just put some lipstick on it and rent it..... last time I bought a property i was all goody goody as well as paranoid and got a mold inspection which now has that property on the hazmat list till i shell out some 20k to remediate it (which mostly seems to consist of guys wearing cosmonaut suits, just like in Ebola land, spraying a cleaning solution, and billing $100 an hour each.....- not to say that mold remediation isn't important, but maybe I could have gotten rid of some of it myself before calling in the mold specialists.) 

Steel wool usually does the trick, coupled with insulating foam spray for the larger gaps.A good cat goes a long way.It is normal for a place to be rid of mice for a year or so and then have one or two come back when it gets cold out.

I want to spray it on every shirt I own, my car, my shoes, my dog, and my 4 & 6 year old nephews!

Can't say that I have a good answer I'm the kind of guy that would get those little pink flags and the pink construction spray and identify every place I seen poop.