tricky one ! a doula is a good idea, regardless of home or hospital birth....but cannot deliver the baby!
IM- she will give you one to one care for this last part of your pregnancy and obviously throughout labour and birth
re the 'they have to send someone' - yes they do BUT, there was a Mnetter who ended up having to go into hospital for this very reason, so it can happen,
you can of course refuse to go in as you are entitled to a homebirth, and the community midwives should be there to cover it.....
if your area is a high home birth area, they should be able to deal with this situation
be worth seeing ig you can find an IM who can take you on as you are 32 weeks already!
a doula can support you at home, and keep you going, and support you, and perhaps even liase with the hospital when you are in labour if there is an issue with the home birth
it is not your fault there are not enough midwives, and if you have the funds to get an IM, then go for it, but the PCT are obliged to provide midwives for a homebirth
i;d get in touch with the head of midwifery and stress your desire for a homebirth