I understand a lot of those variables, but I don't think they're quite as black and white as that. Reamp boxes are used all the time with great success.
Yes, they are actually Black and White. It doesn't mean that reamp boxes cannot be used with great success. A lot of things that change, distort and color sound are used with great success. If you want to try it out - by all means, go for it. I just think that it is important to understand that they do alter sound.
In your case, you have a DI box, and most DI boxes suck. They don't have high enough impedance, headroom, introduce distortion, cut lows, etc. Then your signal goes to an unknown interface. Then you send the signal to your AFX. Somewhere in the process, you get what you call "fuzziness" and ask whether introducing another device, which is mediocre in terms of transparency, will help. It's hard to say, but probably it won't. Maybe your fuzziness is just clipping somewhere?
And by the way, analog reamping is by far THE most demanding usage of an audio interface. To get good results, it has to have outstanding dynamic range, low noise, handle high levels, have low distortion. Does your interface have that all? Or is it some Focusrite thingie?
Is your DI good? If you try to reamp that DI track digitally, does the fuzziness go away? Maybe the problem is with the recording?
Also, how do you use those pedals while reamping?
I think that the more details you provide, the easier it will be to identify the problem so that somebody can help you with it.