Well perhaps a question. Why exactly is the weight of your bike a problem? Do you need to carry it up stairs, or load it on a bike rack? Do you need a lighter bike, or do you just want to build a bike? Build many bikes if the desire comes to you. It's fun!
What I'm trying to say is, riding around a sprawling city like Houston, I'd think going the other way some might be worth it. Longtail bike, able to easily carry longer range battery, and or more cargo back from the grocery. My current version of this weighs in about 100 pounds with a 700 wh battery aboard.
Of course, I'm obviously now a complete convert to the long bike idea. The comfort level of them is so much better than short bikes, and to really replace a car you do need to be able to carry more. But they do suck if you have to carry the bike!
Of course a light bike such as you have does have it's place. Ideal if you have a short commute you do often enough.
5 mile round trip to school or work, something like that. Or the last mile thing, where you put the bike on a bus or in a car for some of the trip. Like you bike to your ride share meeting place, or ride share and then bike the last few miles to your destination. Or maybe you need to fit the bike into a closet once at work, or some other small space.
Anyway, I'd be tempted to just make that frame into a very light single speed and just pedal it. In season I mean. Not in the afternoon for the next few months. Oddly enough, I actually have more pedal bikes on the property than e bikes. Hard to believe for a guy like me.