Hmm can you get hold of a relay with a slightly higher resistance coil? I was going to suggest the LM311 but it's maximum output current is 50mA. It's not a big deal as you could use a buffer transistor, it's just a cleaner/cheaper design without one. If not, it's possible to configure the LM311's output as an emitter follower so it drops a couple of volts which will reduce the relay voltage to 10V and current to 45mA but it's nor best practise.
I'll have a look tomorrow, I'm off to bed now.