Since it seems like a cumbersome job to walk the beam on PR2, I calculated the necessary combination of optics to walk the beam on PR2 without affecting the beam position and angle on BS and ITMs. I put this combination in INP2 of the WFS output matrix (as INP1 is being experimented for WFS).
You should be able to, say, give INP2 WFS filter an offset to manually walk the beam, and/or you should be able to route one of the POP sled QPD signal to it to servo the beam position on PR2.
Calculations
IM4:
You turn IM4 by theta0 and the beam is deflected by 2*theta0.
PRM rotation:
Assume that the beam was perpendicular to both AR and HR before IM4 was rotated.
After IM4 rotation, in order for the PRM to retro-reflect the beam, you tilt the PRM by theta1 so the incident angle becomes 2*theta0-theta1.
The beam angle inside the PRM relative to the AR face is therefore (2*theta0-theta1)/n.
The beam position on PRM is L1*2*theta0 where L1 is the IM4-PRM distance (ignore the thickness of the PRM).
In order for HR side to retroreflect, the beam angle should match the HR side angle:
(2*theta0-theta1)/n = L1*2*theta0/R
where R is the ROC of PRM HR.
theta1=2*theta0*(1-n*L1/R).
PR2 and PR3 rotation:
M0=ABCD matrix from IM4 output to PR3 output.
M1=from PR2 output to PR3 output.
input vector at IM4 output is inV=[0; 2*theta0].
PR2/PR3 rotation of theta2/theta3 is represented as [0; 2*theta2] and [0; 2*theta3] at the output of PR2/PR3.
theta2 and theta3 are determined by the following equation:
M0*inV + M1*[0, 2*theta2] + [0, 2*theta3]=0.
Parameters used:
ROC were taken from nebula web page (-10.948m, -4.543m and 36.021m for PRM, PR2 and PR3).
IM4-PRC distance was roughly eyeballed to be 20inches from D0901083.
PRM-PR2 and PR2-PR3 were taken from T0900043, i.e. 16.6037m and 16.1558m respectively.
I flipped the sign of PR2 component for PIT (but not for YAW) due to the way the local coordinate is defined for SUS.