I had a tall rig too.
Based on your description, I would suggest a few things.
First of all, double check the mast rake. 5 degrees is a lot of rake, way too much. The mast should have 0 to 0.5 degrees of rake. If you hang a weight from the main halyard, in no wind, it should cross the boom about 1-3 inches away from the mast.
The rake (and sail trim) is about right on that rig when you can sail close hauled (at about 28 degrees apparent wind angle on the windex), with about 15 degrees of heel, and the tiller at about 3degrees off center line.
To make the math easy, that’s about 0.6 inches off center x the length of the tiller. So, if the tiller is 60 inches long, the end of the tiller would be 3.0 inches off the centerline. (See correction below)
The boat sails fastest and best at 15 degrees of heel, but has very good manners when gusts hit and heel it further. If you get hit by a huge gust while going up wind, you can momentarily ease the traveler to hold your course,
. Alternatively, you can let the boat round up gently, by easing the tiller a few degrees, and feathering her into the wind, slightly stalling to reduce power.
It doesn’t take a gorilla to control a Catalina 27 TR. they’ve got great manners!
On edit . The sin (3 degrees) = 0.05, not 0.6. So a 60 inch tiller would be 3 inches off centerline with a rudder angle of 3 degrees.