Henry
As you say the Pegasus low pressure and high pressure spools have always rotated in opposite directios to minimize any gyroscopic moments in the hover. Given the simple non autostabilised reaction control system used on the P1127 to control attitude in the hover if gyroscopic couples had existed the thing would have been impossible (rudder would have made it pitch and pitch would have made it yaw for example). Bedford, Merewether and Robin Balmer (the controls and aero man) are all dead so I don't know how much the US experience counted. My feel is that it only confirmed what they already realised and so insisted on with Bristol before the first Pegasus was designed.
The engine men were naturally reluctant to have contra rotating spools because this hugely increased the inter spool bearing speeds to numbers outside their ken.