When the opponents interfere over your ace ask or key card ask, you have two new steps available: double (or redouble), and pass. If the interference is a bid then they have also taken away one or more steps. We are interested in whether the net result is a loss of bidding space for the responses.
What I suggest is the following.
If the opposing call is a double or a bid 1 or 2 steps above the asking bid then no steps are lost. We use pass as the first step, double/redouble as the second step and higher bids as the 3rd step and beyond. We won't call this DOPI because for Optional Minorwood the first step is unrelated to the number of key cards.
With higher overcalls we revert to DEPO (Double = Even, Pass = Odd). For Optional Minorwood this also means that the first step (to discourage slam) is lost.
Two examples with 1430 RKC Blackwood:
After 1♠ - (3♦) - 4NT - (5♦),
Pass = 1 or 4 key cards
Double = 0 or 3 key cards
5♥ = 2 without the queen
5♠ = 2 with the queen
After 1♠ - (3♥) - 4NT - (5♥),
Pass = 1, 3 or 5 key cards (an odd number)
Double = 0, 2 or 4 key cards (an even number)