Two books which you might like to consider when planning this:
Scottish Hill Tracks by Scotways ISBN 0-95466735-0-6
The Drove Roads of Scotland by A.R.B. Haldane ISBN 1-874744-76-9
These show the old drove road (used to move cattle) between the Falkirk tryst and the border. The most obvious route (from Edinburgh area) would be Balerno – Cauldstane Slap – West Linton – Romanno Bridge – Peebles – Gypsy Glen – St Marys Loch – Tushielaw – Craick – Teviothead or Peebles – Innerleithen – Yarrow (Minch Moor) – Ettrickbridge – Hawick.
90% of each of these options is still available off-road. As regards south of the border, I’ll defer to more knowledgeable folks.
Edit: Check out Fay Godwin too….http://www.faygodwin.com/books.html