Very nice! You're right about using the Defense sword (found in the Waterfall). It's equivalent to RUSE, which will be especially helpful in the final area, with potentially enough inescapable battles to otherwise use up all L1 charges before Chaos. Also, WALL isn't necessary in the final battle, since the Ribbon grants protection from everything. (Only XFER can negate that protection and it's not in Chaos' spell rotation)
Having completed almost all of the solo party configurations, I can say with confidence that the worst party belongs hands-down to a solo Thief with no class change. Mages, at least, have defensive or offensive magic to compensate for being otherwise relatively weak. BB starts off slow, but then becomes virtually unstoppable later on. Fighter, of course, has great offense and defense.
Thief, on the other hand, has the worst of all worlds.. no magic at all and weak weapons until the very end. The only thing he can bring to the table is high HP, in the form of over-leveling. Extremely so against Astos, which is needed to have time to hopefully deliver the 4 or so critical hits necessary to win. With non-TAS luck, that's typically Level 20+.
After that, it's mostly downhill, though Lich still isn't easy. The nice thing is that most enemies will run from the over-leveled Thief. :) Of course, the Zeus Gauntlets, et al (including the Defense Sword) are the great equalizers for the second half, though being stuck with the Dragon Sword or equivalent until end-game isn't very fun.
The final assault, however, even at L50, is hit-or-miss, considering the "gauntlet" (ahem) that must be run of fiends and tough, inescapable battles. With no escape magic, the Masmune, which is a must vs. Chaos, has to be collected on every attempt. For Chaos, run-enders are CRACK, SLO2, CUR4, and unlucky damage amounts both for and against. It's pretty much just 2 RUSEs via the sword and hoping for the best while he hacks away. :-p
As Ninja, things are exactly the same until class change. FAST will tip boss battles in his favor. Especially for Chaos, with the power of the Masmune and FAST's ability to counteract SLO2, should it hit.
Even after all that, it would be interesting to see how low TAS-levels of luck could take things.. perhaps less than an L50 finish. :)