As OP, I still feel that this combination is not legal with RAI. Full attack clearly states you cannot take movement and do a full attack. It doesn't say anything about move as an action.
Dimension Door works similarly. Bladed Dash would merely let you charge and get one extra attack per the spell rather than a full attack. Regarding the spell as a "special action" seems broken and at odds with how most other similar mechanics work.
I'd hope this jank crap gets FAQ'd, but I suspect it never will. As many other cheese combinations, such as the Shield Master that takes no attack penalties while dual wielding shields.