What are these?
Do any of them pass through Edinburgh with the exception of direct XC trains to Glasgow Central?
http://www.scotrail.co.uk/content/rail-sail-belfast
The ticket is valid between Plymouth and Ayr by rail.
Ayr is not a routeing point, but Plymouth is.
The applicable routeing points for Ayr are Kilmarnock and Paisley Gilmour Street.
The available walk-up single fares for Plymouth - Ayr are:
SOS +Any Permitted £234
SOS +Via Dumfries £234
SVS +Any Permitted £219.40
SVS +Via Dumfries £211.30
SOS Via Birmingham £206
SOS Not Via London £206
SVS Via Birmingham £201.30
SVS Not Via London £201.30
The fares for Plymouth - Kilmarnock are identical.
The fares for Plymouth - Paisley Gilmour Street are few:
SOS Via Bristol £212
SVS Via Bristol £205.20
Kilmarnock is therefore a permitted routeing point.
Paisley Gilmour Street is probably a permitted routeing point, but you must travel via Bristol.
This turns out to be significant, because if you are travelling from Edinburgh, then you will probably want to catch the Stranraer train from Glasgow, which passes through Paisley Gilmour Street, but not Kilmarnock.
So:
if you want to travel via Gilmour Street, you must travel via Bristol.
The maps for Plymouth - Paisley Gilmour Street do not include LONDON. They are:
BD+ZZ+FD
CE+BS+ZZ+FD
BD+CG
CE+BS
SW+CE+BS
SW+MW+CG
WE+MW+CG
WR+MW+CG
SW+MW+BS
WE+MW+BS
WR+MW+BS
SW+CE+BS+ZZ+FD
CE+NE+EG
SW+CE+NE+EG
I think you could reasonably argue that the route Plymouth - Paddington via Bristol, then Euston - Carlisle, Carlisle - Edinburgh, Edinburgh - Glasgow, Glasgow - Ayr is permitted on maps BD + ZZ + FD, but this could be argued against.
Also valid via Bristol:
Plymouth - Bristol - Newport - Crewe - Carlisle, then again via Edinburgh and Glasgow, or Carlisle - Glasgow (via Carstairs or Kilmarnock) - Ayr
Plymouth - Bristol - Birmingham - Carlisle (via Manchester or Warrington, Stoke or Crewe) - and then as before is also permitted
Plymouth - Bristol - Birmingham - York - Edinburgh - Glasgow - Ayr
Plymouth - Bristol - Didcot - Birmingham - Carlisle (multiple routes as before).
Easements permit doubling back between Didcot and Reading, typically.
If you want to use LONDON routes, then you must go with Kilmarnock as a routeing point, since Plymouth - Kilmarnock has LONDON as a route.
In this case you have the option of Plymouth - Exeter - Waterloo, or Plymouth - Paddington, or various variations along this for the London leg.
From London, you can do the following:
Marylebone - Birmingham
or Euston -Birmingham
Birmingham - Carlisle via Manchester or Warrington, Stoke/Crewe, as before
or Euston - Carlisle not via Birmingham
or
St Pancras - Leeds - Carlisle
Then from Carlisle, either
http://www.atoc.org/clientfiles/File/Maps.pdf#page=1
Carlisle - Kilmarnock - Ayr
or Carlisle - Glasgow (on the main line, not via Kilmarnock) - Kilmarnock - Ayr
or
Carlisle - Edinburgh - Glasgow - Kilmarnock - Ayr
The map is a little confusing, but Edinburgh - Glasgow - Kilmarnock - Ayr does not double back, so is permitted.
Or you can do:
London - Edinburgh via the Midlands or East Coast line.
and then again Edinburgh - Glasgow - Kilmarnock - Ayr
or even
Edinburgh - Carlisle - Kilmarnock - Ayr
You can also the 'via Bristol' routes above, but instead of travelling Glasgow - Ayr, you would travel Carlisle - Glasgow - Kilmarnock - Ayr, Carlisle - Edinburgh - Glasgow - Kilmarnock - Ayr, or Carlisle - Kilmarnock - Ayr, as you felt fit, and you would be able to avoid Bristol on the Plymouth - Reading - Birmingham - Carlisle route.