I think you're overthinking things a bit
I'm glad you've replied to this because we do need a bit of balance, but this has to be one of the least helpful comments it's possible to make in the middle of a focused discussion. The concept of "overthinking" is absurd: you're either thinking about it, or you aren't. If you are, then that process can go on for a short time or a long time before a decision is made.
I would say "overthinking" only really applies if the thought process is still continuing
after a decision has been reached. At that point, yes, it's not desirable to do any more thinking. Since we haven't yet reached a decision, then thinking needs to happen, in whatever quantity individual people within the discussion feel is appropriate.
As you can probably tell, I don't like being told I'm overthinking things

I do mostly agree with your viewpoint, though - i.e. does the idea really need to be pushed further, or is it perfectly fine as it is? This is what we're trying to answer.
Not all ideas are good, and even good ones may just end up not fitting in.
Agreed, hence the discussion

The Batter as-is and the Grenader as-is are good skills.
Again, agreed. I'd personally be happy to implement the Batter in its originally proposed form, but people seem to think a ranged Batter might be a better idea. Rather than create a separate topic or introduce another possible skill to the list, it seems better to introduce the idea into this discussion.
If we repurpose the grenader a bit, we could modify the grenade arc so that it begins horizontal, then continues into the same original arc
Strongly disagree here. The idea isn't bad, and it would definitely allow the skill a bit more versatility, but it would also make no real sense and is counter to what we expect from a classic lemmings skill: one action, one direction.
I strongly advocate against any changes to the Grenader ... if the Grenader's arc is flattened, it becomes much weaker, in my opinion.
Agreed, I don't really think we should change the Spearer or Grenader.
Similarly, adding knockback to the Grenader would also make it worse
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Knockbacks should never be a byproduct of a skill that you would often rather use for something else
Again, agreed, the idea of adding "knockback/flinging" to
any of the detonation-based destruction skills isn't an idea I like at all, tbh. Moreover, this is also the reason why I wouldn't want to give the Batter (or a ranged variant thereof) any terrain-destruction ability; it just feels too messy of an idea.
If we do decide we want any kind of flinger skill, that should be the skill's main purpose.
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The beauty of the Batter - or a dedicated Knockback Bomber, or the Bazooker we're currently contemplating - is that they would only or at least mainly be used to fling lemmings around
The "mainly" here is what's de-railing the current proposal a bit:
we need to be 100% clear on what we want the skill to do. If fling lemmings*, then that should be
all it does - no destruction crater**.
The question, then, remains: do we want this skill (i.e. lemming flinger) to be ranged or not? I'd honestly be happy with either.
Let's agree to focus the discussion back onto this particular question, and rule out any proposals of any skill that
both flings lemmings
and destroys terrain.
*It could still kill Zombies - this can be seen as an equivalent action to flinging a regular lemming.
**Spears and Grenades being able to kill zombies and pop balloons is an exception to this, and has been made because it doesn't add too much complexity or unexpected behaviour. It's a clear action with a clear result, which can be judged just by looking. For the reasons that Strato mentioned regarding Bazookas & Flingbombers in L2, combining terrain destruction and lem flinging is one of those "steps too far" that L2 took; let's not go down that route.