#3
Right, indeed the B-25's did not have a bass player during the first years. It was Kate playing the low keys, but the specific Rock Lobster sound was from Ricky's Mosrite guitar. I read that he used to put only 3 strings; that is evident if you listen to Private Idaho.
#4
Ricky Wilson played a various amount of strings. He had G and B strings in the B and E slots and he had those two strings tuned in unison and he used Drop D tuning often, Although perhaps a step down or half a step up depending on the song. For Running Around he used Drop D and the treble strings were tuned down to E! Other songs such as Give Me Back My Man, Private Idaho and Devil In My Car are in more regular tunings though. The guitar tuning for Rock Lobster would be similar to this:

D *
F
F
C *
B
C

Not sure if it helps you or not seeing you wanted the bass but if you wanted to tackle it on guitar there you go. And for this song you don't tune any strings up, you tube them down. The strings marked with * are not used.
#5
Perhaps a Fender Bass VI might be able to cut it? That has a pretty guitar-like tone to it.