It sounds to me like your partner really wants to be pregnant. Sure, 6 tries seems like a lot, but it really isn't. Your extremely high fertility on round one probably makes it seem extra long, but as many folks here can tell you, 6 IUIs just isn't all that much.
If your partner really wants to carry (and it sounds like she does, I think the "trying together" is a way to take the pressure off. If she wanted out completely, she'd be encouraging you to take over completely), I think you have an obligation to support her in this. Think back to how many family resources would have gone into your getting pregnant with your first, and put that into this for her. I'm guessing you would have easily gone way more than 6 tries before switching up.
I say all of this as a mom who "went second" in our family, after my wife conceived on her second cycle trying at home ICI with frozen. (I mean seriously? Who gets pregnant that easily??!!). I really *really* wanted to be pregnant, and her easy fertility compared to my long, painful, irregular, often anovulatory cycles was hard to handle. I felt like my try was always about to disappear. It didn't. She wasn't jonesing for my shot. She was supportive. But it wasn't easy, and I saw starkly how the pressures can converge to make that "second try" disappear so easily.
Others might not agree, and obviously much of my own experience is informing this response and your partner might not feel nearly as strongly about wanting to be pregnant as I did, but my gut reaction is that the right thing to do is for your energies to go towards supporting her in achieving pregnancy herself, supporting her if she needs a break for a couple cycles, and not jumping into that space yourself.
I wrote here about the pressures that can take that second try away:http://firsttimesecondtime.com/2008/...-switcheroo-2/
Not sure if any of it rings true for you guys, but it might be worth a look.
No matter what, good luck.