I won't give a detailed account of my opinion on reopenings and the like, but I think it might be useful for everyone to see a map of the area with all the historic lines shown. It should certainly explain why these proposed diversionary lines will probably be too expensive to ever reopen. Bear in mind, most of these were little-used, single-track lines even in their heydays.
The black line is the Waverley line.
Grey lines are current railway lines.
Light blue lines are historic lines.
Purple lines are historic lines preserved as footpaths.
I've added some annotations to make things a bit clearer.
The problem is that to even get to Hawick they need to reopen at least half as far again, over what isn't a particularly direct route. There are only two stations worth reopening in between - Melrose and St. Boswells - and each only serves a town of around 1,000 people. Hawick itself is a decent 15,000, though.
Hawick to Carlisle is the same distance as Edinburgh to Hawick, with a grand total of 2 settlements en route worth giving stations to - Newcastleton and Longtown. Newcastleton has around 700 people, and Longtown about 3,000. I would propose that any reopening diverges from the old route at Newcastleton and heads down to Langholm (pop. 2,500) instead. At this point it would join the old branch line back onto the Waverley, and onwards towards Carlisle. There are literally no other populated settlements in the area at all. That's to say nothing of the fact that I'm assuming all of this is even possible, given what might have been built in the towns since the closure. I think it should be obvious that any reopening south of Hawick is a complete non-starter for passenger services, as they'd be carrying hot air around for half of the journey. The type of service that would run on here would only likely be running between Edinburgh and Carlisle, too, so it's not like things would pick up later or that they'd be carrying through traffic from/to further south. I could only ever see this happening if there was pressing need for a diversionary/freight route, and wouldn't expect to see more than 3 or 4 passenger trains a day each-way regularly south of Hawick.
I would estimate Edinburgh to Hawick at 90 minutes, with Hawick to Carlisle at 2 hours, given the slower nature of the southern half of the route. A 3 1/2 hour journey would not be competitive at all, but as I said it may serve as a diversionary route.
EDIT: Another diversion from the old route might be useful between Tweedbank and Hawick, going through Jedburgh (pop. 7,000) as well. It would add about 10 minutes onto the journey, but would serve a lot more people. Branching off to Kelso would be good, too.