first, I think we are talking apples and oranges here, even tho the OP and another pp are talking 'inverted uterus'.
OP, do you mean that your uterus turned inside-out during the placenta retrieval, and came outside of your body? that is a complete prolapse.
Usually, when care providers talk about 'inverted uterus', they mean that it doesn't sit quite the same way as with most women--also known as a 'tipped uterus', if I recall correctly. But the uterus is definitely all up inside the mom! This is not that unusual and not the least life-threatening.
In any event, I would bet good money that it was the manual placenta removal that led to the prolapse (which is what I think you had, given surgery to put it back in). If your uterus and the rest of your pelvic floor are in reasonably good tone and condition now, I see no reason for planning surgical birth--but I would strongly urge that you either have a homebirth or at least a serious discussion with hosp providers about leaving their **&%$!!! hands OUT of your uterus!
I hear these stories from women--usually at hospital tho occasionally at home: 'the placenta wouldn't come out, so they had to go in and take out the placenta manually'--but it turns out 'placenta wouldn't come out' meant that it didn't emerge within a certain time frame (within 15-20 min), even though mom was fine. Some placentas just take longer. If mom is holding/nursing the baby, and is not forced to be lying down with birth and right after but can sit up and move as she naturally wants to, placentas most always come out! Sometimes it takes an hour, or even more--but this is not necessarily a problem. As long as there is no bleeding and mom feels good, there's just no hurry.
Wherever you give birth, I would definitely make sure that you choose a provider who is NOT inclined to putting her hands up inside your uterus. That is something that too many do casually, and it really can lead to big troubles for moms. In the meantime, do some research on placentas--the 'range of normal time' for placental delivery, the different warning signs to watch for, the difference between 'managed 3rd stage' and 'physiological 3rd stage'. Just to be ready for this aspect of your next birth, and able to make wise decisions for yourself.
If you were not literally bleeding a *great* deal at the time, there was just NO reason to try a manual removal! Even IF you'd been bleeding a lot, there would be other ways to help contract the uterus and encourage the bleeding to stop and placenta to come out.
Ok, I'll stop ranting now
Can you tell this is a pet peeve of mine?