I have seen many teams, including my own, where SO2s have line managed C2s without there being any problems. I can't recall ever seeing guidance re: second tour only SO2s only being "elevated" to this responsibility and can recall at least two newly promoted SO2s taking on civilian line management at this level within one of my teams without any problems.
The issue of travel claim authorisation etc disappeared some time ago for civvies, when self-authorisation was introduced for the lower grades.
Having managed mixed service/civvie teams several times in my career I cannot ever recall the generally used rank equivalence I scribbled above being queried by either "side".
By whichever yardstick one chooses to use, be it responsibility, experience, competence or pay it is extremely hard to equate C2 to SO2, in my view. Frankly, given the ability of quite a large number of C2s it's hard enough to equate them to SO3.................
VP