#1
I know this is probably one of those things you need an actual teacher for, but does anyone have any tips for working on your accent, especially while singing? I lack confidence in singing, and it mostly comes from me hating my accent, it just doesn't match up with my style of music. I could easily sing country, or do a passable Bob Dylan if I held my nose, but I'm not interested in doing that.

Of course, in my own head it doesn't sound that bad, but when I hear a recording of myself or through the PA it sounds like the worst hick-town accent I've ever heard and I'd like to lessen it. I think if I had better control over the way my voice sounds I'd have more confidence in singing.
#2
Sounds like you worry too much, but here's a tip, if you insist:
Imitate your favorite singers' pronunciation.

In my world, the color RED doesn't exist.

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#3
Yeah, your voice always sounds different when you are hearing it through your head.

I think you have a bit of a problem with diction. There are a few sounds which are simply unpleasant when sung poorly, one being a long "e" and another being "r."

I'm not sure if this is your problem though. A recording of your voice would help.
Only play what you hear. If you don’t hear anything, don’t play anything.
-Chick Corea