I drew the load lines for both 12AX7 ( top) and 12AT7 (bottom).
View attachment 1083661
1) I drew RL=100K for 12AX7, I make the operating point at 200V( typical). You can see the region between A and B is very linear, that is the spacing between the plate curves is very even.
2) I drew RL= 22K (red) and RL=100K(green) for the 12AT7. You can see the spacing of the plate curves at operating point of 200V is very uneven. The spacing on the left side of the loadline at 200V is much wider than the right side. There is severe distortion.
Yes, miller effect can be less for 12AT7 ONLY IF you change the plate and cathode resistor to 22K and 330ohm as in my drawing. If you just replace the 12AX7 without changing the resistors as what OP want to do, it will not help at all.
If you look at the uneven spacing of the plate curves of 12AT7, I don't think there is a value of plate resistor that can produce low distortion like 12AX7.
Actually, I am using 6SN7 for my preamp tube instead of X7 or T7. It is more linear, just all around better tube. Problem is it will not fit in the small socket.