It's hard for me as a newbie on a 10-string to wrap my head around the need for another bass string, although I've read some very good reasons that you all have given for it.

Maybe the answer is an 11-string.
"These go to 11."

Vostor's comment about higher notes on his 10-string sounding fuller came as a surprise to me; it seems counter-intuitive. I'm glad I read it, though; I initially thought that playing a C two octaves above middle would sound fuller if played on a "longer" string (i.e., played more toward the middle of the fretboard rather than toward the bridge). But I wasn't taking into account the higher tension necessary to get that extra string a 4th higher.