I'd say stick with what you've got for now and see how you get on. I feel a hypocrite though as I bought an e bike for my commute. It's further than yours at 11 miles each way and I'm 11 years older
. That's my excuse, anyway.
I use flat bars and didn't consider drop bars. I shower each morning and find that I'm still sweet smelling when I get to work. I'd rather leave a few minutes earlier and ease the pace than bust a gut and get hot and bothered.