Bm11/D should be notated as Dadd6/9, you're not going from the key of E into D/Bm at all, you're using pedal tones across the first 4 or 5 chords. Bm add11/E isn't actually what you're playing here either, you're playing E B D B E, a Bm add11 always implies a minor 7, but there's no A here, which does not read towards a B chord of any resemblance. It's an E chord, you're in the key of E even if you're playing the Lydian mode. An E7 chord would fit much better in a passing chord, still won't imply it's the I chord with the minor 7 in there.