it looks very hurried, you can have contigencies due road works, rains, and so but reviewing
day 1 Bariloche Futaleufu approx 350 km min. 5 hours with a fair customs clearance
rafting (midday? noon?)
day 2 Futaleufu- Puyuhuapi 190 km 3,5 hours partly pavel , rest gravel
termas are in a island, (morning?) trek to Hanging Glacier at Queulat, max . 2,5 hours noon?) to Coyhaique about 190 km mainly paved
warning roadblocks due rock blasts from 13,00-17,00 between Puyuhuapi and Queulat, ask in Puyuhuapi for more details
day 3 Coyhaique Tranquilo 217 km mainly gravel 3,5 hours tour to Marble (not Ice) Caves
again warning roadblocks due rock blasts from 13,00-17,00 south of Cerro Castillo, ask in Coyhaique for more details
, same day run to Perito Moreno, here 238 km all dirt road with curves at Chilean side , in total min 5 hours , beware customs close at 21.00
I have less knowledge of the legs Perito- Esquel and Esquel Bariloche but seems doable, it is not a very attractive landscape, unless the leg Bolson Bariloche
The weather is not a issue, at most some scattered rains
In short it is feasible but hurried , you will miss Cerro Castillo a nice town for trekking
in my humble opinion other alternative can be invest those 6 days in Futaleufu- Chaiten-Pumalin Park- Puyuhuapi- Queulat and return by Futaleufu to Arg.