Thanks for the welcome, Pax and lrulan.
After some thought, the guys and I think it's best to do the race on racing bikes rather than on our singlespeeds. It's likely that we'll rent race bikes for 2-3 weeks prior to the race day so we can train and get used to the bikes. Most of the training we'll do on our current bikes though, and I've been totally paranoid about damaging my knees after taking up running, so cycling is my cross-training to balance out my running.
My husband and another friend actually suggested getting a race bike and if I don't like the sport, I could re-sell the bike after the event. I'm not sure if that's practical (I'm 156 cm/around 5 foot, so need a small frame in the land of tall German women) but I'll look around the shops here and also had a read through the forum discussions about bike purchase + smaller frames.
Thank you.