Bees, I need your advice/wisdom. Sorry if this is long-winded!

This week, I bought a Dutailier glider and ottoman off Craiglist for $150! I was super excited because it reclines, locks, etc. The cushion covers were advertised as being able to come off and wash, so I bought it even though it was kinda dirty (not terrible, no big stains, but there are some crusty spots that are someone else's baby's spit up, I'm sure). The fabric is off white, for reference.

Well, only the seat and the ottoman cushion covers come off. The back and armrests fabric doesn't come off, and one of the armrests is one the dirtiest parts of the whole thing!

So, my options: My next, probably cheapest option is to have a professional upholstery cleaner clean them. Never used one, don't know how well it will work! Otherwise, Dutailier has some closeout colors where I could buy completely new cushions/fabric for $120 total. While that's almost as much as I've already paid, it's cheaper than buying a brand new Dutailier glider/ottoman.

Does anyone have experience cleaning their glider cushions? What should I do?!

ETA: photo for reference!