No, do not give any time, they need to move out and if don't, get the writ of possession.

These people have possession of the home as their residence, therefore you have to evict.Do so ASAP, then as soon as you know they were served return with your offer now that they know you are serious.

according to the article  the killer was a convicted felon in possession of a firearm

10 years ago I received a misdemeanor for possession of a controlled substance in the state of MS., everything else on my record is expunged, I have passed several corporate background checks etc.

Meanwhile, if you have control of the property and possession, you ought to be able to put a tenant in after some level of renovation and get cash flow while you clear title.

If you wish to have ownership rights beyond mere possession, you will need to find a way to acquire marketable title.

First auction this Nov-No viewing, no contingencies, DO NOT DISTURB OCCUPANT, buyer responsible for taking possession of property (running off the real owner, me!) 

Priced for quick sale -Quit claim deed issued, ownership rights and possession are immediate."

It also depends on the severity of the offense, possession or dealing, without details, can't say.

Sell the ugly and fix the good after you take possession.