Start with closing the corridor south from Bundendore and then go straight to the airport, saving 20-30min in the process of travel time and build Canberra's station at Canberra Airport where all the services already exist and adding half a dozen trains a day will only add more.
Except that cuts out Queanbeyan which is NSW which im sure will get political. Plus IMV the station for Canberra should be more near the CBD/Civic area anyway to serve the business/government community better. Yes the airport has some business but not all business.
How many of the Queanies use the Canberra train a day now?
The airport is a natural terminus, it has faculties and services the train will never have. Even if you use the train today to do business or govt work, the first thing you hop onto is a taxi or bus.
We are trying to get the Canberra train to Canberra in a time that is actually civilised, apart from numerous realignments north of Bunendore all the way to Sydney, most of it low cost, the most obvious to by-pass one of the slowest section average speeds over the entire route and at the same time save even more by removing the unnecessary track-age to get there.
To appease the peasants, you give them what they actually will use, improved local PT. Close the HR line, hand the track and corridor over the the Canberra govt and throw them a few million to build a LR line to Queanie, job done. The airport will also have land put aside for freight terminal and the current and only customer relocated as well as land for a container terminal.
EDIT:
Its about 2km from down down Queanie up Canberra Avenue which is suited to LR to the HR line. This will cost around $80M/km to convert to LR.
Its then 6km to Canberra Railway Station using the HR corridor which is alot cheaper, say 1/2 the price per km and I assume maybe they can even use most existing track about half of which is dual track and includes a dual bridge. The tracks finish right next to the Wentworth Ave, so perfect for continuing and connecting to the future extension LR.
So all up, you get LR from Kingston to Queanie, around 8-9km for less than a few hundred million. Not bad, peasants happen.
The line from Bundendore to the Airport is now 13km shorter than the current corridor (23km vs 36km) and straighter so trains can actually travel at a decent speed, ~200km/h.
Fyshwick yard can be redeveloped to generate some cash to fund the big picture modernisation.
ARHS can big given some bucks to relocate to Queanie station, with its still significant yard which will be truncated just before the junction where the LR connects and decide if they want to maintain the 28km route to Bundendore which being I assume mostly concrete sleepers and heavy rail should be alot easier than the aging Cooma Line.
Now if you really insist on using Kingston as the HR terminus, you can still run via the airport and come into Kingston from the east, still a much faster overall route.