Very tough decision. I hope a depressed FA market allows the White Sox to resign Colome. I would have have guessed pre Rona plans were to promote Bummer and use the $ elsewhere on the roster after another solid Bummer season. The nerve injury is an additional factor in Colome's retention.
The candidates you mention may be possibilities, though the truncated schedule really hurt in terms of providing significant audition time in late inning situations. Foster has succeeded in multiple roles this year. Heuer has looked very good as well, wish he was used more. Wouldn't hold Burdi's bad outing against him, but would like a full year under his belt before considering late inning roles.
Liam Hendricks is the best 2021 FA closer beyond Colome, likely beyond the Sox' budget. I don't know whether other minor league candidates are in the mix with the lack of minor league games or news, but hopefully the minors will continue to provide the White Sox with additional candidates. The White Sox won it all, though with a more experienced veteran SP staff, with rotating Closers throughout 2005, and push comes to shove this would not be my number one priority this off-season.
Right Field would be my top priority as it impacts offense and defense, followed by making a decision as to whether Grandal is a good fit to catch 120 games, or whether a three position rotation between Abreu, Grandal, McCann and Vaughn is best. In a perfect world, the Sox would have signed two OFers instead of Parrot and Grandal, and Jiminez would serve significant time as DH. Would upgrade the defense and keep Eloy's bat in the lineup without continued lost time due to injuries in the outfield.
I do like Grandal's pitch framing, and unfortunately the truncated season limits the time he gets to work with the staff this season (hopefully the postseason adds a few dozen more opportunities ). I think the writing is on the wall and McCann will leave, Collins gets promoted and the money, if used, is for RF and Pitching.
And thanks @Chicago White Sox for pointing out the two RP omissions, Heuer and Burdi. Both will return, eliminating the need for the FA RP.