Would distant defense work with blade tome?

Nope.
DD is giving COMBAT buff, and combat buff(invisible buff) don't work with bladetome. Only visible buff (hone/fortify) work with bladetome

Bladetomes, the one case where Defiant (barely) > Brazen (not saying that other A slot skill aren't better though).

I can confirm that spur/ward/goad/drive type buffs do not work on Bladetome using GOlwen. Oddly enough, atk buffs provide a double bonus i.e. +4 atk provides 8 extra damage. Fortify/Hone/Rally/Dance related buffs (Axe Azura) are the way to go for blade tomes.

Tactic bonus would work on flying/infantry/armored type units using blade tomes, however, tactic skills specifically exclude cavalry type units from their effects. So it is possible to get a blade tome unit under the effect of several Tactic skills at once and with more flexibility than Hone/Fortify skills. And remember Atk tactic would provide +6 atk which translates into 12 extra damage.

I think you misunderstand tactic skills. You must have 2 heroes of the same movement type, or less, on the team. so you can have 2 infantry, 2 flyers. Or 2 infantry and 2 cav. or 1 of each, or 1 of 2 types and 2 of 1 type. lots of possibilities.