.....I personally don't feel a medium strength (judged accordingly to compensate for the person being checked size) body check is pushing it. Following the letter of the rule, you aren't controlling the other person or laying a hand on them. With that aside, I don't feel it is an overly unsafe move, unless done INCREDIBLY unsafe and at that point... ya we should know what to do.....
While this is how I feel, there are a few vets in my realm that just do not like, let alone follow the grappling rules. In the fact that they do not consider it ok for an armored fighter to even grab the handle of an unarmored fighters weapon, including spears
I remind these fighters that this is NOT how the majority of the Dag community feels and that is their personal decision and to not get butt hurt when someone does it to them, whether at our practice or at an event....
This is how I feel for the most part.
I've also came across "veteran" dag players who've gotten butt hurt from me grabbing their weapon shafts and exposed handles (as well as shields) while armored saying that "its grappling" but I've had to disagree with them. So would be nice to let those people who think that, know that they are wrong

(unless its a house rule or something)
Now while safety for others is my first concern, I am a bit of a rough Dagorhir player. I would like to see some leniency when it comes to grappling in armor, especially if when two armored combatants are locked in combat and are less than a few inches apart or already touching. While I know it highly depends on what kind of armor is being wore and what's all going on, I'd be nice (for me and others I'd guess) if we were allowed to grapple once up close and personal and if everything is done in a safely manner.
I do see a few issues with this though.
1) Simplicity. You either can or cannot grapple in armor, adding in a gray area or other exceptions complicates the ruling.
2) Playability, it makes leather and other armors more powerful because you can grapple if needed. This leaves out poor plate and other mainly metal armors I'd guess.
3) Safety is a semi issue, but we all know that if armor touches your opponents body they explode. Especially metal knee and elbow cops.
I know we all have our preferences, but it would be fun if armored players were allowed to grapple to an extent as long as safety came first.
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In the previous Blackhawk scenario, I'd say shove him out of bounds with your hands or turn whatever weapon you had in your hands horizontally brace with both hands and shove, if you wanted to be fully in the clear.
So, yes to hand/forearm shoving, no to shoulder checking (although a body check with an unarmored area might be okay), no to grabbing his shoulders, and yes to either shoving him or killing him with your weapon.