Hi mitchsirk,
I like playing the Best of Putting challenge too!
I am at least one person who has only used a putter. I have only used the WGT>STARTERS Starter Putter and unlimited WGT Starter Ball for all five of my Best of Putting Scores (August.-December, 2013) so far, and I do not plan to ever use wedges!
There are different suggestions on how to use a wedge on that hole; if you chose to use a wedge, you'll probably have to adjust your shot selection depending on the type of wedge you use. I am not an expert at using wedges on the green, so my advice is only for using the putter.
When I played my first Best of Putting Skills Challenge, my goal was to finish below 50.00 total. As I got better, I lowered my target score to below 20.00. I suggest that you set a static goal like this for yourself to achieve. Do not fret about what place you finish, just focus on your target score and try to better it.
For me, the goal is to get it within 10.00 on Challenge 2 in order to have a very good chance at finishing with a total below 50.00 (to the best of my knowledge, everyone receives a Diamond Skill Challenge Cup for scoring below 50.00).
So far, my best score is 14.06 in December with the Starter Putter and unlimited ball. I did this by aiming to finish around 6-7ft from the cup on Challenge 2 (not trying to ace it). I had a 7.33 on Challenge 2 and a 3.19 on Challenge 8, the two hardest challenges in my opinion.
After buying the very precise PING 2010 Redwood ZB Putter (L72+) in January, I have had numerous lip-outs and aced Challenge 2 on seven different occasions (here is one, and another—links may become inactive), but ruined my score on the next holes.
Acing Challenge 2 can be done without a wedge (I even did it with the imprecise Starter Putter once), but it is very tough, so I do not suggest that you try to ace it at first. Aim between the trees like in the image below and go to about 30-35% power with a 150ft scale (if your putter has that). You can use avatar movements (avatar movement: the putter's movement backward as you increase power on the swing meter) to determine 30%. To the best of my knowledge, with the 150ft putter, each avatar movement is 10% power.
You currently have have a more precise putter than the Starter Putter I had, so you should be able to consistently get within 10.00 on Challenge 2. It is important to note that the wind affects your putts, even the low winds such as 2mph.
Let me know if this helps,
JMan