I did some quick calculations based on the
NPIC technical fact sheet and the
Sawyer product information page for their spray and it would appear that you would need to consume about 5kg of this product to achieve the lowest LD50 oral dose.
I couldn't find a risk level for permethrin as a carcinogen, and would be interested to know what you have been able to find out in your literature reviews.
I did note that IARC suggested in 2014 that further research should be a high priority following the release of the 2012 NCI Agricultural Health Study. That study identified five pesticides of interest - chlorpyrifos, coumaphos, fonofos, phorate and permethrin - in relation to increased incidences of prostrate cancer identified in the (quite large) study population, and permethrin may also be associated with increased incidences of multiple myeloma. Previously (1991) IARC had assigned it to Group 3 (not classifiable as to its carcinogenicity to humans).
It seems to me that regular exposure to permethrin and other insecticides in an agricultural setting is likely to be quite different to the sorts of exposure to consumer permethrin based products on the camino. I am not suggesting that one should ignore taking precautions when applying this product. Follow the directions, take care disposing of any waste and clean up properly. But the evidence that I have seen does not suggest to me that one should stop using it as part of other arrangements to prevent bed-bug bites.