GCE Core Rules feedback and suggestions

I don't see why not. Frankly, I think you can land a stikk on top of the barricade with just the -1, but once you go to the other side, then cover applies.

It's not a perfect system, since the -1 from cover of a unit is the same as the -1 from targetting the ground, but template weapons are fairly rare in gorka, and they are supposed to supercede cover somewhat. At least thats my take on them.
 
How does this interact with a multiple engagement fight?
The simplest way to check is, as you resolve HTH for each mini, you check:

Am I in base-to-base with an enemy?

Yes: Then you don't follow-up, activate the next mini.

No, I am not in base contact: Did I make the killing blow?
If yes: Make a follow-up
If no: Then you don't get to follow-up, move to the next mini.

Because HTH has to be resolved 1 mini at a time, this is likely your best check.

Just remember, mini's only participate in one fight per turn. So if you followup into basecontact with 2 more minis, that is taken care of on the next turn with no charge bonuses.