Cubs love to pitch up with power, especially if a little (or a lot) overpowered.

Since most R/C models are overpowered ("experts" may differe there... but they generally have more than they really need. ) Its not suprising that it pitches up as you add power.

think how long a SCALE take-off would be for that Cub... probably 6 times what you use for your longest. Think what the climb rate is for a full scale Cub... nowhere near what you get from your model.

The trick of shimming under the trailing edge... its sort of like putting 2 times the angle in down elevator deflection. It trims the model for a faster base cruising speed. The change in incidence also is appropriate for reducing elevator trim needed due to... excessive power.

Your landing nose-overs are another symptom of having more power than needed. You get used to the plane flying fast... and slowing it down for a NICE 3-point touchdown just at stall speed (cranking full up elevator just as the wheels kiss the grass) gets scary if you don't practice flying SLOWER. The closer I get my tripe to that perfect 3-pointer... the less trouble I have with it when landing.

As for the CG... its possibly dead-on, as you think it is. I'd just practice flying the Cub... like a Cub instead of a whizz-bang speedster.