The game has been out long enough and the Dodger / Ohtani are popular enough where I'm sure plenty of others have done what you're trying by now..... so my guess is you're just overlooking something. I'd be very surprised if this was a glitch only being discovered in late July.
I unfortunately can't offer much help since I have never played with Ohtani or any other two-way player, but my guess if you're just missing something and someone else will be able to solve this for you
Something like this that is a little confusing would be great to have laid out in a manual. That being said, hopefully one of these non-OOTP employees can lay it out for everyone else in their non-valuable free time
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