Ha! I was just having this conversation with my doc. I also am someone who has desperately struggled with sleep most of her life (finally getting handle on it after years of hard work!), is a caffeine addict (tho fortunately much less so now), and for whom the last cigs before bed and first ones in the morning were most important. And of course my doc would always bring up the fact the nicotine is a stimulant and should therefore make it hard to get to sleep. But there's another side to nicotine addiction, which is that feeding the habit can be relaxing (probably mostly just psychological), which can help us get to sleep.
Personally, what I've found really interesting is that while I never noticed the stimulant effect of nicotine in analog cigs, I DO notice it now with vaping! I kind of think of it like the nicotine in analogs being muddled in with so much other crap that actually makes you tired (CO, for example), that I just couldn't perceive the nicotine pick me up. Now without all the tiring garbage, it's obvious.
I still find the act of vaping before bed very relaxing, but am trying to keep it to a minimum so it doesn't affect my sleep or sleep onset. I think switching to lower nic content juice (maybe even 0mg!) before bed is a really good idea.