Considering that folks who build websites charge upwards of $1000 a day, $300 for a transfer sounds reasonable, since you know that rebuilding it yourself will take "lots of time."
I don't really know the details for GoDaddy, since I'm not there, haven't used the easy-build templates. Of the dozens of websites I've built, I coded them all as HTML 2 or HTML 3.2 and uploaded (or copied, inside the corporate intranet) them to my web servers. Mine don't didn't do anything fancy, they just present information.
Without knowing how to actually code for the web, being at mercy of templates and not even knowing how the templates work, paying someone who does know how sounds reasonable.