Your chaeto doesn't look like it's dying but rather accumulating detritus and maybe some cyanobacteria/algae. I have run gfo with chaeto before sure, just realize they are competing for phosphates. I've only done it when my phosphates were extra high for one reason or another, then took the gfo offline and let my chaeto handle it at normal levels.
On another note, I would strongly recommend sectioning off your chaeto somehow from your other equipment. It looks dangerously close to your skimmer in those pics and could easily get pulled in and cause your skimmer to overflow, among other things. If you don't have a separate refugium section, you can use eggcrate covered in netting or make a bag out of netting (sealed with zip ties or something similar) and let the chaeto grow in there, trimming once it fills the bag and starts to grow out of it.
I put GFO Reactor Offline, and will monitor water parameters. I don't have a separate section for a refugium I will cut some eggcrate and section off the skimmer so cheato can't get sucked up into inlet portion.