Edinburgh & Borders connectivity with D&G, especially were the Gtetna terminal realigned to join.
The borders don't need a railway to Dumfries and Galloway. The Symington - Gala line will never reopen, that's dead and gone.
There is an argument, if you squint, for better connections from the south west to Edinburgh, although for most people, reopening some of the stations down the GSW and having a full 1tph service in each direction from Glasgow through to Carlisle would suffice.
A Borders extension, almost as far as WCML/Carlisle, would bring added potential for D&G connectivity were the GSW's Gretna terminus minimally realigned.
This is also not the way to improve connectivity; trying to link the south west with Edinburgh via a magical mystery tour around the mountains on the old Waverley route would be folly. That would easily be a two and a half hour journey time from Carlisle. At that sort of duration, waiting two hours for the next direct train from Lockerbie would be faster for 95% of journeys.
If you took the hypothetical pot of money that reopening would cost, you could just as easily spend it on reopening Symington and Moffat stations, tag on a few extra EMUs onto the new order, extend some of the loops over Beattock out to 775m, and run a semi-fast stopper down to Carlisle in the opposite hours from the Edinburgh TPE services. I can guarantee it would cost less overall.
'Want some diagramatic examples of my alignment vision? In essence my 4.023km/2.5mile track construction would feed/connect the Larkhall, Uddingston (inc' WCML) & Edinburgh corridors but I've illistrated a more ambitious Northern continuation. Meanwhile, voila!
Realistically, there's never going to be an extension of the line beyond East Kilbride. It's not worth it, and it's an easy change in Glasgow.
If you're looking for better connectivity from North Lanarkshire and south Glasgow to the east of Scotland, then the Shotts line provides a very good service now from Waverley to Central; I'll often get the fast services if I need to be at Central. With journeys at an hour and change, and services generally much quieter than the Falkirk High line, especially in summer, it's a nice jaunt.
If you're after more connections between North Lanarkshire/south Glasgow and the Forth Valley, then the solution is binning off the Cumbernauld extensions from the Argyll line services, and running a 1tph shuttle in each direction between Stirling to Motherwell, with new stations at Abronhill and Bonnybridge.
The questions one must ask when getting the crayon out, in order, are;
1. Is there a genuine problem here, a lack of connectivity, that needs a solution?
2. Have you looked at all the alternative solutions that could be implemented for much less money, and discarded them?
3. Is there a demand that would justify the cost of a new solution?
4. Is building a new railway, with all the costs and problems inherent in that, the right solution?
Only if all the answers are yes, then is it a plan that will be pursued. In this case, I don't really see the demand, I can think of several alternatives that would cost less, I don't think the number of passengers it would benefit would outweigh the cost, and I'm not sure building a new alignment and running brand new services is the best idea for this hypothetical problem. I'm afraid it's probably not going to happen, although I do enjoy the process of crayoning myself, and I can completely respect the art; I did it for a living and I enjoyed it thoroughly.