What are your levels? Usually they like them to be above 10, but just because they're lower doesn't mean you can't still have a home birth if you want. It's always your choice. The added risk with low iron is that if you were to have a PPH, you would be much sicker with already low iron (because PPH usually causes anaemia after the fact). So that would suck, but you'd still feel just as unwell in hospital and need extra intervention. Usually in that case, they would offer you a transfusion (you would have to transfer into hospital for this, but it wouldn't be an emergency thing, just they'd let you come in when you're ready and you could probably go home the same day) and they recommend you take high potency supplements for a few weeks after birth. It sucks a lot, but it can happen wherever you are and isn't specifically a risk for home birth. The good thing about home birth is you are significantly less likely to have a PPH at home than in hospital, so actually being at home might be protective for you.
You also have plenty of time to take iron now and get your levels up. My levels were great in pregnancy (13.9 and 12.1) and I didn't have a PPH, but I still became anaemic after birth. I didn't opt for the transfusion though it was offered to me. I started to feel a bit better just after taking the tablets on my own, so decided to stick to that unless I started to feel really unwell again. I took high potency iron tablets (the 200mg ones, maybe twice a day?) plus one Spatone sachet and 500mg of vitamin C at every meal (so 3x a day). That brought my levels up in about a week. Postnatally I was measured as an HB of 6 and then a 9 a bit later, so really low! I had a home birth and I'm not sure if actually my levels were low to start or they dropped after (like I said, iron was good all pregnancy and I didn't have a PPH).
You definitely can bring your levels up and you don't need them to re-test you. You can birth at home with any iron levels anyway, though they might advise against it. It's ultimately your choice 100% and they have a duty of care to support that choice. But if you feel well, I wouldn't be too worried. Even when my levels were a 9, I felt horrible. I could barely walk without passing out. Every time I stood up my heart would race so fast I could feel it pounding in my chest and I thought I was going to have a heart attack. If you are going about your day otherwise feeling fine, then your iron is high enough that it's keeping you healthy and feeling good and that's a good sign. But don't sit on your laurels. Get yourself on the really high doses of iron (Boots has them - ask for high potency iron tablets, usually they are 200mg per tablet), add in both Spatone and Floradix, and take loads of vitamin C or drink a small glass of orange juice with each meal.
I hope you are able to get your levels up and have the home birth you've always dreamed of! I think a private lab sounds like a great option (assuming it is available where you live) if your midwife won't retest. I don't have any input or suggestions that haven't already been mentioned so I will offer a virtual hug instead. 
