I'll be honest, I never read that thread. It came up during one of my Dwarf Fortress-induced lulls in posting, IIRC. Also this thread's title is way more interesting. TBH, I'd be willing to bet that there's enough CL boosts available if you cheese it out enough (you need a total +70, so as I see things working that means you need a base +14 to general CL, and if you've got that then this is only a discussion about the magnitude of your CL rather than your ability to kill TBoS). And with the number of actions you can rack up, you can probably still drop enough MDJs to reasonably stand a chance of breaking all those AMFs the TBoS has up. So I'm not exactly opposed to that, just what I see as an erroneous interpretation of Sublime Chord and a small piece of Master Spellthief. I'm going to do the CL math again, though, because I see the OP is different from what I quoted earlier.
Pre Sublime Chord
Bard CL 1
Spellthief CL 1
Wizard CL 14
Post Sublime Chord (Sublime Chord is based on class levels, NOT caster level; the arcane spellcasting class in which you have the most levels is Incantatrix, arguably, so we'll go with that)
Bard CL 11
Spellthief CL 11
Wizard CL 11
Sublime Chord CL 11
Post SCM (Increase Sublime Chord caster level, as normal, dragging everything else up)
Bard CL 14
Spellthief CL 14
Wizard CL 14
Sublime Chord CL 14
Via Master Spellthief, all classes use sum of these when casting
CL 56
Then, Items and Buffs, each of which grants +4 to final CL for each +1 it ordinarily grants, since it applies to each class separately. Discounting the Bead of Karma until somebody explains how we're getting it to work for our character that can't cast divine spells. It's +16 otherwise, though.
Ioun Stone (+4)
Ring of Arcane Might (+4)
Create Magical Tattoo (+4)
Don't think I've missed anything. So that leaves a final CL of 68, with an improvement to 84 if the Bead of Karma has a trick to allow it to function that I'm just missing. You may see significant improvement if you start Sublime Chord as soon as it's possible, beginning with level 11, since any +1 classes can add to that and that arguably drags up all other classes.