The advice is to use the bus, travel via Newcastle or travel on one of the services via Dumfries though. Alternatively, if you absolutely cannot bear to do any of those things for a couple of months, you'll still have all of the normal options from Glasgow and Edinburgh Airports, National Express or car shares. These options are accessible to basically everyone. Those with licences and vehicles also have private motoring.Seriously though, for all the replies, the end result is the same, massive disruption and advice to effectively not use the railway. Fail.
You do raise a sensible question about how long it would take though - no doubt the work could have been done in less time. However, the two key reasons it isn't is because a) it would cost significantly more and need a much bigger staff team to work day-and-night for however long it eventually took and b) this would cause a lot more disruption than blocking it in phases and doing prep over weekends in advance.
The only possible alternative is to build an off-line bypass, then close this area for renewal after that's open. While some might argue for that, the cost would be orders of magnitude larger. Therefore any such bypasses would really need to stand on their own two feet for the benefits they brought beyond alleviating a couple of months work of work. To connect a new line that's already been fully built you still would need to close the main route entirely for at least a couple of days.