2.5 months between BC and Pucon sounds fairly speedy, but certainly within the realm of possibility. You'll want to keep moving, at least to allow for potential mechanical (or physiological) failures. That might mean flying your bike across the gap, for example.
3.5 months down to Ushuaia and back to BC doesn't sound particularly "more relaxed." If your goal is to ride a lot, maybe that'll be ok. If the point is to see stuff, do things, interact, explore, stay open to whatever comes your way, well, not so much.
Your budget is about US$50 per day, which is fine for what it is....but camping doesn't always lend itself to efficiency and speed. That's worth thinking about. I blew out a shock in Suriname, spent a week and some money getting a bodge repair, then finally found a replacement in Guatemala for US$500 or so. I also had unexpected repairs in Texas and Curitiba (along with a slew of predictable maintenance), and if your budget is tight that sort of thing can create havoc.
I'd have a few fallback positions in mind, e.g., can you extend the trip if that looks appealing? Can you skip Ushuaia entirely without serious regret? Etc.
Hope that's helpful.
Mark
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