I too would suggest a short scale model like the Fender Mustang bass or something with a slimmer neck such as a Jazz bass.
With most short/medium scale basses having a short top horn, 1st position reach generally isn't that much better. It's true that the frets are a little closer together. 34-35" scale isn't difficult if you can adopt 1-2-4 fingering. Where most folks go wrong is wanting to play 1 finger per fret and typically have their fretting hand at an angle that makes the same distance between frets a longer reach.
When I started out, I felt the same way you did, until I met a fellow bassist with smaller hands than mine (kinda creepy) that had a few more years under his belt. He gave me the rundown on flexibility and how it relates to being able to play on bigger necks. It's not all related to just playing either. You need to stretch you muscles in your hands. Warm them up before you ever start playing/practicing. It helps, trust me.
