Very briefly butting in, having read your OP, and literally none of the 40 replies since (sorry!).
3 DC? 4DC? Really, once over 2, The Deed Is Done
I readily I admit I was 'Two and Stop!' (which we did), but the only fly in the ointment I can see is your expectations regarding having The Girl.
She and you may not gel in any way. Any projecting you might be doing on that person may collapse into a morass of hatred (sorry!). And, again, IMO, girls appear to be way harder than boys if things go wrong.
I was. My mum and I never got on (dad and I did!). There was no 'girly' stuff at all, to the extent, latterly, I never shared any of my 'personal' medical concerns because I knew she's go a-bonding with her late middle-aged women friends in sharing it! Whose DD's were my friends, who I chose not to share with.
I had my DC in Australia, where we could afford private (much more affordable than here!).
I Had DS1 (at 36). All 'good' (the little screamer!).
1yr 3 mo later, pregnant with DC2. Due at my 38! Had an amniocentesis as 'an older mum'. My Obstetrician (so the person I saw through all the pregnancy) was as old school as you could get. On amnio results day, he happily told me, all was well (in that department). I asked re sex. He said "Now, Mrs Tansie, you must demand I tell you the sex" (I don't have to!). I was non- plussed, so went along and demanded. He turned his family photo towards me (mum, dad, 2 boys) and said 'You, like me, are blessed with 2 boys'.
I now know he expected me to collapse into a mither of tears. No GIRL?? Some of my friends at my baby group, apparently, DID. Feeling robbed of a child of the opposite sex, or, a GIRL.
My reaction was 'Yay. Boys, by and large, more simples'.
Go for the 4th, but please don't lay any expectations on her. You may well yet bond far more with DS2. Or 3. Or 1.
Don't 'keep' no 4 because it's a girl, but do it because it's a fourth child.
Then ride that bus!