I went from 0.87" to 1" on my '73 sb Dart and I'm stepping up again soon to 1.12" FF bars.
In this day and age, I'm thinking 1" bars should've been 'stock' A-body springs imo.

Shocks become more important when springrates go up, or otherwise the car becomes 'bouncy' when hitting speedbumps for instance.
KYB's have a fairly hard initial bump and not enough internal friction to control heavier springs.
I've got Hotchkis adj. shocks on the front and Bilsteins at the rear which were a major step up in the car's feel and handling.

Specially with a 7" pan I would think you want 1.12" bars aswell.