Say I have a dishonrable Goju Yurishi at a battlefield and he is targeted by Under Arrest. Can I use Yurishi's reaction to move him home so I can move him back into the battle?
I think I can because the rules state: (bolded emphasis)
Interference with costs and payments
If any specific payment of a cost is negated, delayed, or made impossible in the process of paying costs, the player paying the cost may use alternate available sources to pay it, or may choose not to pay it. Example: If “Move your Personality home” is a cost, and the movement home is negated by a Reaction, you cannot choose to move him home again to pay the cost.
If no alternate payment is made, then any costs already paid are not refunded, no further costs are paid, and:
If the unpaid cost is for a card entering play (including entering play as part of an action), it goes back to where it came from. If the unpaid cost is for an action, the action fails, and its effects do not happen. The action is still taken and ended, but not resolved, and the ability that created it is used. If the action was on a Strategy card, the card is discarded.
If a cost requiring a target is interfered with (such as a Reaction that prevents the bowing in the cost “Bow your target Samurai:”), a player cannot choose a new target to try to pay the cost, because the targeting step is already completed.
And "do not happen" trumps negated.