Sounds like you need Google Feedback (more here). It's the feedback tool currently integrated into Google+. Once you click it, it pops up a little toolbox that allows you to "highlight the problem" (which uses the DOM to highlight specific HTML elements, rather than asking users to draw on the screen) or "black out personal information" (so you can easily remove private messages etc. without having to use an image tool).
Why it works well:
Keep the user in the session. Rather than creating a barrier to entry involving taking screenshots, saving images and uploading them like you mention, you just click a few times, type a few lines, and forget about it.
Offer specific actions rather than asking for images. Rather than asking for a screenshot or even using any terminology like that, it just talks about highlighting the problem* and blacking out personal info. Then it asks you to add a comment, preview (using a generated screenshot of the page) and send.
No tech jargon. No screenshots, bugtracking, issues, tickets or other typical tech support crap ever comes up. They simplified the process to essentially what you would do if I were sitting next to you: point it out, tell me what the problem is, and we're done. This is very important.
The only problem is that it isn't a product; Google is only using it internally. I'm sure they'll release it into the wild eventually but for now your best bet is to learn from what they're doing and reproduce it the best you can.