They make the most delicious jam in the world, and I use them in crumbles and pies too - wonderful. Yes, they only have a short season and do not transport and store well, hence the reason they're not often in supermarkets and if they are they're under-ripe and tart so people don't know how wonderful they really are!
I buy them from the local farm shop at this time of year. A former colleague had a large tree in his garden and he would bring in buckets full of fruit to the office and I took them home and made jars and jars of jam, and froze what I couldn't cope with at the time to use later.
Colleagues didn't know what they were - someone said they were Goosegogs!
But they ate the jam quickly enough when I took a jar in with some scones 
Sadly the colleague with the greengage tree left. 
He did say that some years the tree fruited very little and some years there was an absolute glut - probably to do with weather conditions at pollination - probably a bad year this year.
This is a good site for gages etc and they're very helpful http://www.readsnursery.co.uk/products/Cambridge-Gage.html