Melissa,
I had a Yorkie, Josie, that had megaesophagus. The key thing is...regurgitation, NOT vomit. The food and/or liquid sits in the esophagus, because it's more or less flaccid and will not push the food down to the tummy. Therefore, it's not digested and comes back up looking and smelling like exactly what it is...chewed up food. No retching or straining when she regurgitated, she'd just kind of burp and there it would be...her dinner. NOT barf. Usually on me or the sofa, lol. My other Yorkie, Charlie, quit sleeping with her because he kept wearing her food and didn't like it much, lol.
I could actually feel the swelling in Josie's throat where the food was sitting in a bulge in her esophagus. No foamy bile ever appeared because she wasn't sick...just couldn't get food to her tummy. Your Izzy sure doesn't sound like a megaesophagus dog to me, but I'm no vet. Perhaps it presents differently sometimes.
I'll tell you what I did so she could get her food down...sounds obvious and silly in hindsight, but the vet was so pleased he wrote an article about it. This was back in the dark days when they were putting dogs with megaesophagus in centrifuges to force the food down....!!!
Anyway. After she ate, I would pick her up and pat her back vigorously...somewhat harder than you would if burping a baby. Sometimes I'd stroke her throat gently, if I could actually feel a bulge there. Eventually, with luck, I'd hear a big glurping sound when her food finally went down. Pretty much all at once.
She was diagnosed at Angel Memorial in Boston at around 4 or 5 months and they told me she was a goner. Well, she lived to be four, and it wasn't the megaesophagus that killed her. Turned out she had several seriously undersized organs and was a mess internally. You never would have known...she had a happy, active life until her final illness.
All this is to say, if Izzy indeed has megaesophagus...you can deal with it.
Truly you can.
My very best to you and your sweet Izzy. (Sorry, I really didn't mean to write a book.)