Scott, do you have someone helping you learn to fly your plane ?
If so do they think that the climb with added power is excessive ?

Some trainers are designed so that they have a shallow glide slope with the engine at idle.
You fly around the pattern at 1/2 throttle, chop to idle and glide in to land pretty much hands free on the elevator and throttle.
Not a bad characteristic at all for a trainer.

Also if the plane climbs with increased speed this helps you if the plane gets in a nose down attitude, as the speed increases it will pull out of the dive pretty much on its on if you have enough altitude.
Again not a bad characteristic for a trainer.
I have not flown a Hobbistar so I don't know if that description fits or not.

Now for the real question, do you like the self correcting features built into the plane or are they bugging you ?
I personally do not see anything wrong with tweaking the plane to make it fly better, with better meaning to make it fly the way you want it to fly. You should think about all of the various flight characteristics of the plane though before changing anything.

If adding down-thrust will "fix" your climbing with throttle issue the plane will mostly retain its no power glide slope, some of its ability to self correct at 1/2 throttle in a dive will probably be lost, and hitting full power in an aborted landing attempt will most likely be different than it is now, takeoffs will probably be a little harder.

Changing the wing incidence, will change a lot of flying characteristics. This is not a bad thing, but you should think about it.
The closer you get the plane to neutral (no trim change required for throttle setting) it will have less self correction from a dive and you won't be able to just chop the throttle let it glide itself in and then flare just before touchdown, the glide slope for landing will require elevator and throttle management.

Good luck to you.