What exactly do you mean by "breaking point"? Like the point where it becomes unlikely to hit? With the Belt it'd be +13 with the -5, which doesn't seem too bad to me. Without, it'd only be +9, so might be best reserved for Channel Divinity.
Oh I was just spitballing lol, maybe splitting this into two separate character ideas. Another possible variation could be Draconic Sorcerer 6/Forge Cleric 14, sacrificing Paladin features to focus on Green-Flame Blade and fire magic. You'd lose a lot of melee capability against fire immune enemies, of course, but it'd be a good fit for the gimmick at least. :P
Huh, I didn't know Hexblade got Elemental Weapon! That is a potentially interesting idea, although honestly I'm a little tired of Hexblade lol. That aside, it occurs to me that you could squeeze in a level of Fighter there with Sorcerer 14/Hexblade 5/Fighter 1 and get a little extra bang for your buck in the form of a Fighting Style, heavy armor and Second Wind.
True! I think a Sorcadin with a Flame Tongue Greatsword is more what I'm looking for. I like the idea of getting the flight from dragon wings, haha. Of course, at this point it doesn't stand out as a Build so much, but then the realization that Elemental Affinity doesn't really work with Elemental Weapon already kind of put a damper on things. Oh well! It's still nice to have Quickened Elemental Affinity GFB for some extra burst damage.