Only those elements that are outside the scope of the IRC must be 'designed' - in this case the log walls. Any elements that are within the scope of the IRC - dimensional lumber floor joists for example, could still be done prescriptively. And the IRC directly references AF&PA's Wood Frame Construction Manual for species, loading conditions, etc. that are not provided in the IRC Tables.
Short answer, if the joists can be found on a span table, they can be designed prescriptively and the drilling, cutting, boring and notching limitations would apply.