This is going to sound stupid, but after a while of shaving with a double-edged razor I found I could shave in the shower with no lather.

I just wait until I'm done washing and the steam has had a chance to soften the hair, then shave directly in the shower. It took a couple of weeks of shaving daily for my skin to get used to it but now I get it done with no irritation. An advantage of no lather/gel is that I can keep putting my face under the shower to keep the hair soft.

(I shave without a mirror, and then clean up afterwards)

This isn't going to be for everyone, and it certainly isn't as close as a gilette, but I can get the shave done in a couple of minutes.