Is there some reason you need to see it in 'plan'??
I've been working 3D exclusively for 20 years and almost NEVER work in a 'plan' view of the UCS.
also investigate 'UCS OB'ject (E still works for 'entity') for setting a UCS to match an existing object.
For planes that are 'normal' to orthogonal geometry I use
(defun c:ucr () (command ".UCS" "w" ".UCS" "3" "0,0,0" "0,1,0" "0,0,1")) ;; 'RIGHT' side, looking in negative "X" axis direction
(defun c:ucb () (command ".UCS" "w" ".UCS" "3" "0,0,0" "-1,0,0" "0,0,1")) ;; 'BACK' side, looking in negative "Y" axis direction
(defun c:ucl () (command ".UCS" "w" ".UCS" "3" "0,0,0" "0,-1,0" "0,0,1")) ;; 'LEFT' side, looking in positive "X" axis direction
(defun c:ucf () (command ".UCS" "w" ".UCS" "x" "90")) ;; 'FRONT' side, looking in positive "Y" axis direction
and
(defun c:uce () (command ".UCS" "E")) ;; UCS to entity
(defun c:uco () (command ".UCS" "o")) ;; specify new origin
(defun c:ucp () (command ".UCS" "p")) ;; UCS Previous
(defun c:ucv () (command ".UCS" "V")) ;; UCS match View
(defun c:ucw () (command ".UCS" "W")) ;; UCS World
(defun c:uczee () (command ".UCS" "z" "ENDP" PAUSE "ENDp" PAUSE)) ;; spin UCS about "Z" axis to match 'endpoints'
All of the above can be modified to add a call to "plan"
(defun c:ucf () (command ".UCS" "w" ".UCS" "x" "90" "" "plan" ""))
or Mr. Allen's viewsave/restore tool
I am sure the lispy gurus around here can produce a more elegant set of tools without leaning on the (command ...) but these work fer me.