I understand that Dua Tawassul contains statements that directly address the Imams. As such, is it permissible to recite this Dua in the state of Sajdah?
It is permissible to recite Du'a Tawassul during Sajdah because the Sajdah is only for Allah (SWT) and never for any one else but Allah. During Sajda Sahw, we recite (Bismillah a Billah, Assalamu Alayka Ayyuha Annabiyyu Wa Rahmatullah Wa Barakatuh). It does not mean that we doing Sajda for the Prophet (SAWA) but for Allah (SWT) only. Addressing the Prophet or any Ma'soom during Sajdah does not make the Sajdah for him at all but it remains always for Allah (SWT). It menas hat you are talking to them while prostrating to Allah (SWT).
Wassalam.