You start with local traffic within AM and to the nearby towns and
cities.  When the cash cow is giving milk, you build towers.  Down on
the plains they'd be mostly wood, and that's just a matter of carpentry.
Where there's likely to be serious danger of attack, you build a masonry
base.
This is not dragon wizardry -- it can be done cheaply by local labour.
You use lots of work gangs, and out in the country -- it's mostly
country -- you're playing cheap local rates, with a fast-completion
bonus

You'll need about  300 towers to Genua, max.  You don't begin at  both
ends, you begin everywhere.  Every three or five  towers or so you have
a repair/ maintenance tower with supporting buildings, and you get these
done as soon as you can to serve as depots for the others.

Where've you've got even two adjacent towers up and running, you'll be
making a bob or two off local traffic (at a nice cheap rate to encourage
usage.)  Even before all the towers are finished you have guys up there
running a minimal service; the key thing is to be earning.  That means
not a lot of machinery at the start, and you haul that in from one of
the cities and anywhere there's a craftsman who can read a blueprint.

When the line is running all the way across the continent many of the
towers still aren't complete and the operators are working surrounded by
sawdust.  Doesn't matter -- you're up and running and paying off your
debts.

I reckon you could do it in two years, including surveying and land
purchases.  The sites which could well be dirt cheap -- after all, you
could be the first king on your block to have a clacks tower and special
low rates for royalty. Indeed, nearby towns might *bid* for towers.

It's amazing how fast gold works.
--
Terry Pratchett