The 3.71 volts was measured at the first signs of it starting to cut out. It will continue vaping a bit after that. You'll start to notice it doesn't hit every time, especially if you've been hitting it hard. Or it may be off and on. It basically starts acting funky, that's when I know my battery is getting low. If it hits 99%+ I know it's good.
I'd love an extension tube for the P+ that allows me to use a IMR 18650 and the Kick, but the mod would be huge. I'd still use it though.
Still at 3.7v it shouldn't be having any issues at all. That aw imr 18490 should be able to supply enough current to satisfy the kick maxed out to at least 3.3V