copy portion of track to new project

Hi all

We sometimes multitrack record our live sets by just leaving Reaper running.
So we end up with one long project with maybe 15/16 songs on it.
I was hoping to be able to separate these songs out to individual projects -
one for each song.

I started by
1 create new empty project
2 set up new tab and load source project
3 place markers between each song
4 double click timeline between markers to select first song
5 select all tracks - ctrl+ a
(all tracks for first song highlighted)
6 with cursor over any selected item in arrange window
then ctrl + c to copy
7 go back to new project tab and click in empty arrange window
then ctrl + v to paste

This procedure does copy but it copies all the songs to the new project!

Can anyone please help

cheers Phil

copy portion of track to new project