Yes, I know there are loads of plugins and all kinds of options for Oo, but I can't get them to work and I spend more time then I can to admit looking for things italicized in Word which should be italicized in the LaTeX document... it's making me insane. Help would be appreciated so much.
My preferred converter, Pandoc, doesn't handle RTF to LaTeX, just the other way around. It does handle MS Word to LaTeX, and MS Word or OpenOffice/LibreOffice can open RTF files, so you could convert from RTF to docx, then convert to LaTeX from there. And you could, theoretically, use the online Pandoc tool to do that final conversion, but the webtool is limited.
I did find a command-line (not webbased) tool on the GBU website that will do RTF to either LaTeX or HTML. UnRTF. I can't vouch for its capabilities, however. There are a couple websites that offer file upload and conversion, but can't personally recommend any.
It's not a website, but I've had great success with the excellent pandoc when converting (basic) documents. I'm mainly converting from markdown to LaTeX, but the demos seem to suggest that pandoc works from RTF to LaTeX too.