I do partly share the concerns about influencing how you play when you know about certain reactions, but consider the following two scenarios:
* I'm playing Inquisitor Shyloque. I could either round the corner and walk past the building towards my objective, or take a long detour. Around the corner, I know as a player, is the opposing Sgt. Henchman. He is holding his lasgun and has prepared a reaction to shoot me once I enter line of sight. I take the detour.
* I'm playing Inquisitor Shyloque. I could either round the corner and walk past the building towards my objective, or take a long detour. Around the corner, I know as a player, is the opposing Sgt. Henchman. He is holding his lasgun and has reserved a reaction to use as he sees fit. What do I do now?
I'm inclined to say that in the second scenario, just like in the first, my style of play will be influenced (or I might consciously will myself into taking the bad decision, just to prove that I'm not metagaming - which is not a highly desirable outcome either). I wonder if perhaps the difference in actual gameplay might not be as big as we think... but then again, there are probably lots of scenarios where it does matter, too. I suppose, for when it really needs to be secret, you could always just use notes or whisper into the GM's ear, but that's not practical as a standard mechanic. I do think that the option to do it like this should be there though, as it's really just a very extensive generalization of the existing overwatch mechanic.
To end this rant, I've found my opinion shifting somewhat towards your position while writing this. So yeah, there should be a solid system for non-pre-declared reactions.
As to your second point, I'm not 100% sure what you're for and what you're against. Could you re-phrase?
I agree that perhaps splitting the turn isn't optimal - while (in my mind at least) it's the most natural way to extend the existing action mechanic to reactions, it would perhaps be a total bookkeeping nightmare in large games. I do think there should be some possible way of taking multi-action reactions, though - perhaps only as prepared reactions?
However reactions are handled in the details, I'm firmly of the opinion that they should be drawn from the same pool as regular actions, so that'll provide a limitation in and of itself.
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So, new suggestion:
*Prepared Reactions: You can prepare reactions using the 'Ready' Action, set triggers, and make sequences, as discussed in my original document. Perhaps, to reduce bookkeeping, a character can't have more than one multi-action sequence of reactions.
*Reserved Reactions: You can set aside action dice before rolling for actions, and store them (visually indicated by leaving the appropriate number of d6's next to the character's model) for later use. You can interrupt another character's turn, but you can declare only one action at a time to do so. You roll however many dice you want, but any passes after the first are disregarded - rolling more than one die serves only to increase your chances of passing the action, not granting a chance at multiple actions. Failing all dice means the dice are wasted, and you cannot execute the reaction. Should you have lots of action dice left, you can attempt several reactions, but you can only make one attempt to react to each of the acting character's actions - so you can try again, but not until he performs another action.
*As discussed earlier, Action rolls will pass on 3+. Also, when rolling action dice for Reserved Reactions, there is no 'free' action if you fail all rolls.