While Marcus is correct on the currently hosted end ... site is probably setup with user jail ... it's the platform to which one is migrating that needs to be prepped. Case in point ... the db dump you get from currently hosted site will need to be imported into a db on the new. Knowing the settings for my.cnf for the site on current hosting is a plus cause one might need to adjust my.cnf settings on the new platform or experience some 1 step forward 1 step back issues. Things like max_allowed_packets for DB ... and then there is also php settings ... migrating some quite a bit like fresh install of newer in that for a short time php is pushed ... and so is apache if using web interface to migrate.
In order to know, thus make the migration easier, more efficient, which equates to less time ... knowing settings of current site so that at a minimum, those same settings can be put into place on new system prior to spinning up the new site.
I, myself, have been involved in several of these types of migrations and an say beyond a doubt that no two were alike ... exactly. What kinda struck me was the time quoted .... 45-60 hours seems alot. Those are billable hours, yes? I too would want some extra time to address un-known or foreseen issues with the migration, but have never asked for 45-60 hours.
If you don't mind some advice ... ask the person doing this, if they could get your migrated site to be updateble/upgradeable via git. Even if you don't, yourself, do updates/upgrades in the future but contract those out, git would mean fewer hours ... and perhaps less prone to error updates/upgrades.
Am not stumping here to take over the job, mind ya ... ;)
2 cents worth ... I know ...
'spirit of sharing', Ken