It pains me to help a Roots player, but I would say your problem is you don't have enough big threat nukes. This leaves you in a position where you most likely need to win three rounds to win the match if you don't win with, or draw, Gretchen. Also, it means you probably can't afford to bluff with Gretchen if you DO draw her. I would replace Burdock (You are already crippling them with SOA and att manip, don't worry about all stops) with either Lilly or Amanie (don't see these a lot so the obscurity factor might work in your favour, too), OR switch out Burdock for a 5* and ditch Treeman for another attack manip, like Jeto, or heck even another obscure card like Walden (who actually increases the potential damage of your deck). Both will force at least 2 pillz in most situations.
I feel dirty now...
Your cards are pretty well-rounded but I feel, it's lacking in both damage and power. What do I mean? Well...
Power-wise, the cards you'd be relying on will be Tuck, Rico, Burdock, Gertjan to actually win rounds. These cards are at a disadvantage in relatively higher pill fights against All Stars or Ulu Watu. But that's OK.
The highest damage you can deal for your cards is 5, and only 3 cards do that 5 damage. This means that without Jeena as your meat shield/surprise damage or Gretchen as your healer you'll be in a disadvantage against cards that can hit pretty hard at around 7 to 8 (that's actually very common) damage and you'll have to think very hard to counter said high damage cards, predicting when they'll be played and so on.
You can try winning 3 out of 4 rounds, although that isn't a very plausible strategy to rely on. I'd suggest more damage. Amanie will win my vote for this, over Burdock. I also second Nomi Ld's suggestion on having Ojibway, although I haven't played Ojibway very much to judge yet.
Lastly, have you considered going dual? You may miss out on Roots' precious bonus in a 1:3 or 0:4 split, but the only perk of playing Roots in mono is a constant supply of SoA (which can be bad against Stop: Ability cards) and the +16 attack from Gertjan.
Don't trust me too much on my advice, I'm NOT an elite Roots player. On the contrary, I'm actually a pretty weak player. If my advice helps though, feel free to take it.
What you already have is good enough. play a little more carefully (dirtier) you will get there.