The Tengu should have a prop mod on it anyway, and you

HML tengu! Yes, you'll do more dps on paper (and to the BS'es) with the HAM's, but there's more HP's worth of rats in the room of smaller ships, which the HAM's will struggle with. Carry furies for cruiser+ and precisions for the small things.

If you decide to go the BS route, a raven and/or Abaddon supported by either Domis or Oneiros would be your cheapest best bet.

Torp Raven with range rigs and minimal tank, with a RR domi for drone support. Aggro the whole room with the Raven and launch all your drones & set the to guard. Usually with 2 BS and good drone skills. by the time the Raven is done with the big stuff, the drones are finishing up the smaller things.

Abaeddon > Apoc, with proper skills.
Abaddon+Oneiros vs Sansha will outrun any other two ships that you can put together.

I 5 box, but I solo incursions now. Back when I did missions, I wound up with two separate groups, as I was being limited by travel time between gates.

Let me know (or look me up - Zamp) if you have any specific question about setups, ship combos, or PVP.