I have about the same girth (just a tad thicker but not as long as you) and yes, I have found that it can be difficult with some women, particularly if they are somewhat tight and as a result, intimidated by it. Doggy has never worked well for me with any woman. Though Im sure there are girthy guys who have made it work. (Im not a fan of doggy so I never had much motivation for that position.)
1)If you think there may be some psychological issues try her on top and let her run things. More control for her may let her get over the intimidation factor.
2)Talk to her a lot during sex. Many women get off easily with good communication and if you are soothing as well, it may help.
3)Lots and lots of prep work to the point that it actually gets annoying, and maybe even more. Patience and caring is key here. There are both physical and psychological reasons for this. If she sees that you are willing to suppress your instincts to such a degree to make sure she is satisfied, it may help a lot.
4)Try to not thrust much. I found that with my very first girlfriend, who had very similar issues as your current girl, if I just inserted and grinded she could have very powerful orgasms with much less pain.
5)Try making sex less about sexual organs and more about the psychological nature of the act. For example, I have found that positions that allow for very close face-to-face contact, intercourse is less about my penis and her vagina as it is about the two of us and seeing each others reactions to it. We get off on each others reactions as much, or even more than the physical act itself.
I doubt any one of those will work by itself, so you may want to try and combine several together. Lastly, and Im sorry to say, incompatibility is a possibility. I found one girl that it just wouldnt work with, no matter what we tried. At that point, you have to decide if the relationship can work without good sex (if you even want to try and you wouldnt necessarily be a bad man if you werent).