Since the drill dojo's benefit (improved rally and formation holding) cannot be measured i am unsure wether retraining a unit where there is a drill dojo actually works.

you can retrain whole units to take advantage of improved armour and swordsmith,
the unit does not need a matching dojo to do this,
any dojo in a province with armoury and/or swordsmith can pass these benefits onto any unit type. (a drill dojo does NOT need to be present for this)

beware, if the armoury has only a swordsmith and an armoury, and the unit has famous or legendary weapons, when you try to add the armour the unit will lose the weapons, and actually be downgraded to the swordsmith level of the province with the armoury - most annoying.
if the province has no swordsmith, simply an armoury, the unit keeps it's weapon level.

also, the unit MUST be in the province for a season before you add it to the retrain/build queue - the unit can disappear completely, or wind up back in the training queue of the last province where it spent a season, again annoying.

Province bonuses for units (+1 honour in Tosa for Ashigaru) can be passed on to a unit,
add an honour zero ashi unit to the retraining/build queue in tosa and it will gain the +1 honour.

I don't believe bonuses from famous or legendary dojo's or bonuses from palaces can be 'retrained' into a unit,
i am currently playing a campaign where i intend to test this.

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DoragonBarocca of Clan Doragon