There's no way to make it a middle ground, unfortunately.
If you allow some arbitrary nutrient criteria for EBT, then the only thing that's gonna change is that the manufacturers are going to either shift existing formulas, create a variant of that formula to fit EBT, or lobby as hard as satan himself to make the cutoff so pathetic that it's effectively useless.
Read up on literally every single food rating system in the world, like Australia's star system or the EU's nutri-score, it's gamed to fuck, and makes zero sense.
If you add a tax specifically for EBT on junk food, you both have the same issue as above (although you can just say NOVA 4), then you're actually exposing yourself for discrimination, as it would be seen as a tax specifically discriminating against the poor.
A straight up cutoff at NOVA 3 and saying that EBT are only eligible for NOVA 3 or better, you can't pin it as a tax on the poor, it's an incentive for them to buy healthy food. Much easier to defend in court.
And sure, they won't be able to buy "Healthy UPF" like Whey powder or protein bars or vegan bullshit or whatever, but these things are supposed to be supplements in the first place, so they can still invest in them with their meager salary.