Don't you love it when you think "I bet this would work" and then you try it and it totally does? Subject aside I strongly suspect I did not originally invent this method of ending a tablet weaving just because it seems semi-obvious, but haven't seen it referenced in any of the tablet weaving resources I've looked at so who knows.
The technique is reasonably simple, at each row of the tapering section I cut loose the outermost two pattern warp bundles (the ones just inside of the selvedge border cards) then passed the newly free warp ends out through the shed of the selvedge cards before weaving on, weaving the remaining pattern cards in-pattern as I gradually moved the selvedges in and wove out the rest of the warp, finally binding off the last of the selvedge warp with a bit of French whipping. The whole thing honestly seems pretty much solidly secure as-is, though I will probably be tassling the diagonally protruding warp threads just for looks.