Long ago I wrote http://michaelawolf.name/blog/2013/11/02/off-yer-bike-notes/.
What I wrote there still, in my opinion, sound advice. Since then, however, after a frustrating period where I was getting flats every two or three weeks, I changed my tires to Schwalbe Marathons. In addition to being far more puncture resistant, these tires are also slightly smaller. As a a result, my bike is much easier to fold than it had been.
In spite of making my bike slightly slower, the Marathons were a worthy upgrade, all the more so because it’s easy to fold again.
Here, Off yer bike explains another workaround, this one requiring tools. But it looks pretty easy to carry out.