I'd +1 to the several folks recommending an Etrex 20 with a map as backup of course.
This from someone who spent years poo-pooing the things.
As for "memorising" chunks of route I can usually only hold 2 or 3 turns at best and then on the ground apparently straightforward turns/junctions can be more complex than you thought.
+1 also to the comment above about map consulting breaking your rhythm - I find that a GPS has made me "purr" along more, not in a hurry as such but overall faster I'm sure. I think that when I relied just on maps I was subconscioulsy pushing myself harder to the next junction because I knew that I'd probably have to stop/waste 2 or 3 mins there to get the map out, check it, stow it away.
With a GPS you can let the road roll gently beneath your wheels, knowing that you don't have to bother about a turn for maybe 800m, 2km - whatever its magic screen is telling you.
If you plan to use the Etrex 20 for this big trip (you didn't say when) get it ASAP and start studying it, the guidance online, using it for every trip - it takes a long long time to get the best from it.