prevent leaderless O from unhiding outer nested tmux

tmux/.tmux.conf

@@ -57,14 +57,22 @@ bind -T copy-mode-vi 'y' send -X copy-pipe-and-cancel "pbcopy"
 # set -g status-right "#(date +'%A, %B %d, %Y')"
 set -g status-right ""
 
-# Activate OFF mode (hide outer status entirely for nested tmux)
+# Enter OFF mode from the outer tmux: C-Space o
 bind o \
     set prefix None \;\
     set key-table off \;\
     set status off
 
-# Disable OFF mode
-bind -T off O \
+# Reserve C-Space O for leaving OFF mode.
+unbind -T off O
+bind -T off C-Space switch-client -T off-prefix
+
+bind -T off-prefix O \
     set -u prefix \;\
     set -u key-table \;\
     set -u status
+
+# Forward every other C-Space sequence to the inner tmux.
+bind -T off-prefix Any \
+    send-keys C-Space \;\
+    send-keys