Interesting, are you unarmed build by any chance or str based? Because for me (pure run, agi based) the goblins wouldn't leave after kicking, it would take couple of kicks. But i just recalled that i did get a passive that was related to Karryn kicking said amount of times from the receptionist job.
Do you know how much order you get from fans? I would get more order from the job then processed visitors so they must be giving some but certainly not 1 per fan. Maybe it's better to decline fans if you only want order?
Goblin HP range from ~300 weaklings/normal to over ~700 (wanted/rare type), they level up as days passes and # of riots so these numbers tend to go up, but Goblin level up mainly their AGI, not their HP. Some rare goblin type have OP (Overblow protection) so don't bother trying to score a lucky critical on them.
Equip str boosting acc or level up str to up kick damage, dex + accuracy acc and leveling acc to accurately kick them. Agi acc and Agi level to move before them so you can optimally kick them 2 time in a row.
To lure them in, Greeting, Processing Papers and Radio call actions are sure way to RNG trick them into moving forward, let them come right behind Karryn before kicking them (So you can kick them 2 times consecutively). If you kick them as they're next to you, they run away, which is not ideal, Lure them in! (Can only be used if your agi greater than them, and you need a shitload of Agi if you chose the wrong goblin/orc problem edicts, trust me, it's no joke)
About orders gained, it's complicated, but use this simple formula from me:
Papers done - Order gained
1 - 1
2 - 2
3 - 3
4 - 4/5
5 - 5/6
6 - 6/7
7- 7/8
8 - 8/9
9 - 9/10/11
10 - 12
11 - 13
12 - 14
so on, but I doubt most players have time to score more than 12 peoples while dealing with goblins, pure build or not.