The tone of a Bass VI type instrument comes not just from the range, but from the fact that it is a "slack key" tuning. The strings are very loose, and have a certain sustain that kinda goes "whap" up front and then dies off. They give you fret slap with anything but light plucks, and they provide different overtone character than a normally tuned instrument.
To get close to the sound you are after, you are better off with a 4-string short scale bass strung with extra light strings and low action, than you are with a guitar and an octave pedal. Spend your octave pedal money on a used Squier Bronco instead. You'll get closer to what you want. Most of the range played by the most famous of Bass VI (or similar instrument) songs is accessible with a standard short scale bass. And you'll get close to the attack by using extra light strings, set low. The strings that come on Broncos are probably light enough, but you can go about .010" lighter, if you want, by using the bottom four strings from a light gauge Bass VI set (.086" E string, IIRC).