It makes me so sad to read your post. 
Please don’t blame yourself. It’s not your fault, and what mom wouldn’t wait and try and hope that her baby would take a bottle? You’ve done everything you possibly could!
I can definitely relate to the sadness you feel when you see other moms feeding their babies. My little guy is 20 months old and I still get pangs of sadness when I see babies happily drinking from bottles or nursing. It was such a struggle with both of my reflux babies and it’s just very, very sad, even though we didn’t have to resort to tube feeding; so I can only imagine how sad you must be.
Now to answer your question about if they ever get over it. Yes, I think they can and do. Myles loves his bedtime bottle now and he screams for it when he sees it. This started at about a year, even though since the age of 7 months he would not take a bottle at all except (reluctantly) that one bedtime bottle. He never ended up on a tube (thankfully) but I had to spoon feed him all of his breast milk and formula because he hated the bottle. Now he loves the bottle! Ellie also began to enjoy the bottle once her reflux was gone.
Does she take a pacifier? I think Heather (Bryce’s mom) said that it’s good to give them something to suck on while they are being tube fed so they associate sucking with feeding.
Is she on any meds for her reflux? Does she seem to be in pain?
I hope and pray you get a call for Speech Therapy soon. I will keep Cassie in my prayers. 
