So, admittedly I'm coming in late but...
C botulinum is a gram-positive rod that can be found in dirt. There it lives, happy in its anaerobic environment, enthusiastically producing an exotoxin that is very, very nasty. There is an immunization that requires three doses, but if memory serves, it doesn't cover every variety.
Essentially, it interferes with ACH. The anticholinergic symptoms presented above are classic for botulism.
Because it lives in dirt (and doesn't have a geographical preference), it can contaminate food grown in that dirt. Add poor food handling, and you can have a nice outbreak. Of course, it can be present in fish and some other snacks.
In addition to the excellent questions FM asked, I'd want to know if these men had been wounded, scratched, etc., and if so, was it in the same geographic area. I'm looking for wound botulism vs. foodborne botulism; abx vs. HBAT. I'd also want a good CN/neuro exam. +/- bowel sounds? A patient with + BS can be purged somewhat if it's foodborne.
Given the rapid onset, I'm leaning toward foodborne botulism toxin A or B. Question of the day is, how did it get introduced into the troop's food? Was it deliberate, or poor food handling? Who else may have been exposed? Are they accounted for?
If it were wound botulism, abx are no problem. I've got an aid bag full of PO and IV abx that will kill C botulinum. Make an incision, debride the wound, hit them with PCN, Clindamycin, or even Flagyl, monitor them carefully and get them to a higher level of care which hopefully has HBAT.
For foodborne botulism at this stage, I'd consider charcoal/sorbitol, an enema, HBAT if it were available (and it's likely not, so evac to a higher level of care), blood and stool samples, and very close monitoring.
In an ideal world, I'd want EtCO2 monitoring, SaO2, the works on these folks. An ABG would be great, but... Not likely out in DurkaDurkastan.
As the paralysis progresses and dysphagia becomes more pronounced, or I see signs of hypoxia, I'd seriously consider RSI and mechanical ventilation, though this is of course problematic with several pts and limited resources.
Botulism isn't hard to cultivate, and would cause a serious problem if unleashed as a bio-weapon.