Yeah, that Battlemage’s is a thing of beauty! 
I talked a lot about the Claw/Fragment combo because, since I tried it myself, I had a lot of input to give, but I do want to emphasize that I personally believe Battlemage’s is a really good sword if it had some good legendarized affixes (which yours totally does). Its main drawback is that it makes it hard to scale crit chance, but Peak of the Mountain can definitely help make it work!
I disagree with Psojed’s opinion that spark charges are a bad match for Spellblade, though; Runemaster might have some very good elements for them, but I strongly believe they can work on Spellblade very well, too - especially since you can grab a lot of the good elements in question from the left side of Runemaster’s tree, even as a Spellblade.
That guide is a few years old, so of course many things have changed since then, but if you’re interested, here’s the guide I mentioned about my own iteration of a spark charge / lightning spell trigger Spellblade. Always give priority to what I said in my previous message over what I say in that guide, though - for instance, I use Static in the guide, but like I said before, I don’t think it’s that worth using now.
If I manage to build up the motivation for it, I’ll try to make a planner for the few changes I mentioned about your build, but no promises, I’m extremely tired these days. :')
Feel free to let me know if you have more questions, and don’t hesitate to @ me if I don’t see your answer - here or on discord (@Lunomica there as well).