I can understand having a speech impediment that doesn't go away while singing.
I have an issue where it sounds like I'm slurring my words, so I often overcompensate. I also always sound stuffed up even when I'm not. I'm still working that out, I was just wondering if the lisp was induced by singing with over emphasis or something.
Good news is that i can't hear it when you do death vox so... maybe think of it as if you were doing those?
regardless, I'll post some technical stuff later with examples, just so you can hear what I'm talking about. I dunno if my technique is correct, but my voice is still here and I've been doing it for years.
Often the trick is to not over force it I've found. If you just pretend like its not actually that big a deal it comes out a lot cooler and easier on your cords of vocals I think.
Anyway, keep up with the diaphragm stuff, that is REALLY the key. As far as the speech stuff... I dunno. "She sell seashells by the seashore?" I'm sure its at least a little fixable, at least in the studio, no one could really fault you live I suppose. I mean, on recordings I can barely tell that Tarja from nightwish has a huge finnish accent, but live it shows through really harshly.
Just food for thought, keep it up brando.