Tmux key binding issue

I found the solution to mimic the original behavior under screen (only including relevant parts of the config as the rest is just window dressing):

# set prefix key to ctrl+a until I have time to adapt
unbind C-b
set -g prefix C-a

# send the prefix to client inside window (ala nested sessions)
bind-key a send-prefix

# toggle last window like screen
bind-key C-a last-window

# navigate through windows like screen
bind-key C-a-n next
bind-key C-a-p prev

Chaining together the key sequence directly was the solution. I didn't realize that you could actually do that, but it works perfectly, and I can still keep the send-prefix option (which I was concerned was part of the problem).

Tmux considers any key-presses performed while the ctrl key is down to be of the C- form. You could simply add bind C-p prev and bind C-n next to get the same effect though.