Hi OP,
We're in a similar position. Why have two kids, 4.5 and 2.5 years old and just moved cities, living abroad from family. I'm currently due in two weeks, or four weeks max, iykwim.
First labor was inducen post-dates. Second time around, we had a list of about three or four expat friends who had babies the same age as my eldest, who were willing to come and collect, or receive our older kid when I went into labour. They all lived relatively close, in the same city. We pitched it as a childcare swap thingy, and we paid them back in staggered babysitting, a few hours here and there. It worked out really well for us.
This time around, like I said, we've just moved city and don't know many people, and obvs it's that difficult time of year. I've just spent today asking a heap of people that I don't really know, what it consider to be a massive imposition. However, I also know that I will find it very difficult to relax enough to let go and labour, if I'm not relaxed about what's happening withthe kids. Our priority is that it be someone that our kids already know, and they are few and far between. The most obvious choices being: mothers of I similar aged kids; crèche staff; grandparent-types; known babysitters... So today I asked our cleaning lady and offered her money and she was clearly delighted to be asked and very happy to be available, said to let her know as soon as I thought things were kicking off and spent a few minutes playing with my kids and telling them they might see her when the baby is coming. This was so comforting to me. Even though I know realistically we need a few people lined up, just in case. I also asked in my sons crèche, and have been offered a list of contacts of the ladies who work there who are available. Again, we obviously are expectingto pay for this as a "babysitting service", however, for me the peace of mind makes it worthwhile. Another person we plan on asking formally, and who has already offered to be available is a friends mother, with whom we have a pretty good relationship, and who helped us out with emergency childcare for a week previously. Said friend may also be around, depending on if it's an actual holiday day, and has a kid the same age as our youngest one. I'm sure we can pay them back in kind.
One of journey pm others will then come out to stay with us for a while after the baby arrives, but I'd like a few days to be a new family together before that happens.
So, that's it really. I won't be happy until we have a substantial list of people available. We are expecting to have to pay, and I understand that may be difficult for you, but there are ways to repay people that isn't straight money, and it sort of is to be expected when you live far away from family.
As it was with our second kid, we called my mother when I was, as I thought, a fairly long time into labour, and she arrived at the hospital a good two hours before the baby was born. Which was a bit weird...
I wouldn't hesitate to help out someone in he same situation, im ion, im sure almost anyone in a similar position would feel the same. I think you should ask people, as many as you can. Express that you don't mind if they can't, and give them time and space to make excuses if they need to, and it think you'll be pleasantly surprised at how people will be happy to help out.
I did read somewhere, I think it was Ina May, or maybe Michel Odent, that second time mums after start labour at night time, just after the older kid/so have gone to bed, because that's when she's most relaxed, and also gives the longest uninterrupted stretch before needing to find someone to look after her older kids. It was true for me, contractions started strong and regular at ten pm, just that my second a labour was very long!
Either way, best of luck and I hope it all goes great for you!!!!