I dunno if it'll help but watch the consistency of the food you syringe too. You want it liquid enough to hydrate and "flow" but not runny enough to maybe accidentally give too much in a push or have it go everywhere. I go with a "pudding" texture, it's heavy enough for their tongues and mouths to handle without being dangerously runny they could easily aspirate.
80cc's I THINK is a little over 5 tablespoons? When I had to do Fena for a freaky week, I eyeballed 1/2 of a 5.5 oz Friskies can, added 3 to 3.5 tablespoons hot water (not boiling but steaming) and blended in a food processor until smooth. Was a great consistency.
Then later in the day, you can blend the other half with another 3 - 3.5, etc. It's a slow process.
I agree on something for the tummy - Pepcid or Cerenia, but I remember you said the subQ is iffy for your budget.
Does your baby drink flavored water at all, like if you add tuna juice? I've made catnip "tea" that's worked - plus my own broths. Sometimes they won't eat food they but will lick up "flavored" water, to help too.
Did your vet tell you about warm compresses for the abscess site? It encourages blood flow, which brings white cells, serum, etc. to the area quick to help flush it out in addition to your squeezing - it might help make it more productive too. When you squeeze it's actually good to see "some" blood, the bright red kind. Not a lot, just enough.
I went through this with my male Irish Setter, Laddy back in the day. Another oddity - dunno if it transfers to cats but for Laddy I had this one tangerine/orange candle, and whenever I burned it he would settle down and it seemed to take his mind off the abscess pain. Worth a shot maybe?