So I don’t have this exact problem but I have one fussy about his bit. I am looking for a Weymouth for his double bridle and have my eye on the Trust InnoSense ported, fixed side plastic version that is flexible (medium, not hard). I think the thinner version looks promising and I might consider the snaffle version for your issue.
I have that same Fager bit and he didn’t love it. He weirdly liked a heavier one, the Mikmar Cupreon with a ridged link eggbutt. I never would have picked this bit in a thousand years but it came on a bridle I bought used on FB Marketplace and it turns out he loves it and is happier with more contact than any of the other ones I tried, including a few of the Neue Schules, Fagers and HS bits. It’s heavy and thick, but he randomly feels comfortable in it. He is naturally very light mouthed so I actually needed one I could take more of a feel of his mouth with, and this is the one. Who knew? It isn’t as expensive as some others so maybe worth a try.
The turtle top is very popular and my other horse likes it. She goes in that happily, so worth a try especially if you can borrow one! She’s a good egg though and not picky at all.