For sixer your gonna have the problem of very wide neck compared to guitar. Making playing a lot of guitar stuff impossible unless your very very creative with how you do 4 and more string chords etc. The EADGB string aspect of the desired tuning is quite simple. Is the higher 5 strings of normal 6 string bass with high B instead of C. But that means little less tension for the B string. Getting a suitable string for the high E string might be difficult from many brands.
Guitar pups wont work for such a bass since theyre not nearly wide enough. Which brings us back to that very very wide neck compared to guitar.
I'd suggest getting five string bass and tuning it EADGB. Narrow enough necks are available with brands like Ibanez.
For example of bass doubling guitar parts theres stuff like Jonas Hellborg on bass with John Mclaughlin on guitar.