I am deliberately not reading the thread. I will read it, but I wanted to post without bias, if that makes sense.
I recently thought about something similar (not the same). I have a friend who is gay (and who has a partner), and I also want another baby, and we thought we'd try together. It didn't work out (medically; we did IVF and the first try didn't work), and for various reasons, it was clear that another try wouldn't be a great idea.
I don't know how helpful my perspective is, but it might be?
I imagine other posters have asked about practicalities - how will you do it, will it be IUI or IVF or what; how will you decide (if it doesn't work) when enough is enough; how do they plan to compensate you for it. In what contexts would you/they terminate a pregnancy? (This is really important!). Etc.
What I didn't expect, was how strongly I felt pushed around by hormones. Granted, I did IVF and it's a ton of hormones. But, I did not expect to feel emotional about my child's potential father, nor did I expect to feel so swayed by how he felt. How would you feel if (for example), you miscarried and they felt very differently about it from you? Or if (sorry, it's horrible), you became pregnant but a baby had a condition that meant you, or they, felt you should terminate - and you disagreed?
Would you be able to discuss a situation where you spent at least some of the first year with the baby? Personally, I would not have a baby I couldn't spend at least the 'fourth trimester' with. It's quite a doable thing, if they are willing - but it makes the attachment harder for you.