The repetition game that existed in Umineko was prominent because of how arguably open-ended some of the locked rooms would’ve been without making certain guarantees about them, due to the lack of information about them given in the actual narrative for understandable reasons. I generally try and rule out most of the basic options in the narrative itself, and rule out the need for repetitions necessary to establish that an impossible crime really is seemingly an impossible crime. So in those respects, the repetition game should not be necessary. (Of course, when I miss something, it’s usually in one of the first few theories suggested, so it gets taken out rather quickly.)
Next are the repetitions designed to rule out variations, as you’ve suggested. I generally go out of my way to make my reds rule out most if not all of the main aspects of a theory when responding in the first place, hopefully doing that in the process. If after that the player tries a variation that I didn’t realize could circumvent the red, I try and hammer it in. I don’t like being deceptive and haggle you over a minute detail - the point is always that you understand the concept and the mechanics of the crime. Once I’ve seen the charade is broken, as I’ve said, I concede. But a theory must be formed, and it must be done given the constrictions of the narrative and the previously given red.
Which brings us to the information fishing point.
It just happens too often.
And generally it’s not even the player’s fault! When options seem few and far between, it’s easy to just want to confirm the culprit’s actions that you believe must be the case given the red, but then hit a dead end under that assumption, so you turn to confirming once and for all to know where to focus.
It also doesn’t help once the players start getting a bit frustrated. If I, for example, refuse something because I, for whatever reason, just see no point in repeating or think the narrative can sufficiently answer the question, the player if low on options, will probably start throwing (arguably ludicrous and far-fetched) theories until I back down and am forced to repeat it. If nothing else in part because I want to get the game back on track. Yet, once that happens, the same thing carries over for any future repetitions.
I don’t consider it a terribly awful rule to have, in any case. If they want me to deny a certain point of entry, they first must propose a workable theory that doesn’t fight against the narrative or what’s been previously established. If they can’t, then what’s the point of repeating?
So, for example, in your own theory, I could ask you this:
Battler’s plan for a hole in the table relied on Genji putting the letter where he did. But what guarantee would’ve Battler had for that happening? Given that it was an instruction Kinzo seemingly gave only to Genji, you can’t really claim that Shannon could’ve just told him. Or, I could question how Battler’s arm could’ve been able to reach the place where the letter was put on the table. After all, when you put your hand below the table, you can generally only go a little beyond your elbow without looking bizarre and suspicious. And I don’t recall Battler ever conveniently dropping a fork…
…Yet, given the fact that this is the second time a hole in the table has been suggested, instead of keeping you off-track and leaving room for more attacks on this front, I’ll indulge you. The table features no secret compartments, coverable holes, secret mechanisms within it, or anything of the sort - it is a perfectly ordinary dining room table.
Er, sorry for the rant there.