It's rather unlikely that you could successfully statically link against multiple C runtime libraries - you would run into many symbol definition conflicts which would at least produce voluminous warnings, and only a reckless engineer would ignore them.
With depends
, I would make sure to use the dynamic profiling option, to check all dependencies for dynamic CRTLs they load. If doesn't turn up anything, I suspect your problem is elsewhere.
I would suspect your problem is elsewhere in any case, though, as DLLs with C-level APIs shouldn't, as a rule, rely on shared state in the CRTL - most commonly the memory allocator - and should have adopt a standardized protocol for cross-API memory management, such as caller-allocates, callee-uses, or passing in memory allocation callbacks, etc. In other words, multiple CRTLs in the same process is normally not a problem due to correct use of a memory management protocol.
For transient failures, I would suspect multithreading or heap corruption.