Pics would help show what you've got. The OMM will not work as it's dependent on the thru-axle for mounting the rack.
Surly makes a solid, tough rear rack. Link:
https://surlybikes.com/parts/rear_rack
Back when I installed it on both the front and rear of my Specialized Fatboy, they called this rear rack the "Surly Nice Rack", take that for what it's worth. Provided you have upper and threaded eyelets in your seat stays, this rack should be the ticket. The rack itself is powdercoated steel and it uses some nice stainless steel hardware to mount the rack to the frame. Here's a pic of that Surly Nice rear rack mounted on the Fatboy:
The lower stainless steel rack mount stays have the ability to slide up, into the lower rack stay, so you can fine tune the fitment. Note the way I mounted the Surly top rack mount stays.....I used a seat post clamp that comes with threaded bosses to accept the stainless top rack stays. You can pretty much find this style seat post clamp anywhere. I picked up mine from a business called Problem Solvers.
I wanted a full touring capable fatbike, so with the rear rack in place, I set about with the front rack. I used the same Surly rear rack (note: Surly does make a front-specific rack, but I liked that rear rack design, better). The front rack would support a dyno-hub powered light, while the rear rack had a mounted dyno powered tail light. Here are all the components, minus the hub, and minus a two part paint on the light mounts. The original Fatboy fork was carbon fiber, but I utilized a Fatboy aluminum fork which accepted threaded eyelets from which the rack stays were mounted......
End product, front and rear racks, dyno hub lighting system, complete Ortlieb bag system for front and rear racks.....even trips to the local supermarket if needed. This Fatboy is a 2015 model, which used rack skewers, like your Giant. Hope this helps!
