I'm stuck in a little corner of the galaxy whilst the AI is exploring like crazy.

I haven't seen a range increase yet. Any tips on how to get that range increase?

as mentioned in the other thread, you can use outposts to extend your range.
as for technology, all the 'range increasing' technology is in the Physics section.
note also you can use 'warp lane amplifiers' in your ships to make them be able to fly a good distance past your dotted range (this comes by default in scounts, colony ships, and outpost transports - but you can put them in your warships if you really want). When you have a scout or colony ship selected, hold down the right mouse button to see their extended range.

At the top of "select a research list" is an icon like this This lets you see all the techs. Look in the physics tree for techs that "increase strategic range to X parsecs"

You can also lick on the Physics icon (blue atom) to see a list of all the physics techs (which includes the two range-extending techs).