So, you already have the ideal frame, which is built for urban commuting, but you want something else? The Bad Boys are tough bikes, and light. SSing one of those is easy, as you already have the EBB, and will save you a fair few quid.
Plus, I’m assuming it already looks a bit ‘used’, which is a bonus, for locking up in town. The tattier the better. Bionickev off here had an old tatty RM Blizzard for round London; looked sh1t, but was a really nice bike.
So, as above, fit some chunkier tyres to your Bad Boy (26 or 700c?), and then you’ve got the perfect machine.
Or, do you just want another bike? 😉