I don't follow your connections.
Following what I think you are saying.... If someone was flying a VNAV, a flight that cannot be done under positive control or IFR, according to what you posted it would be ok to not treat the TRSA as class C.
A VNAV can be done under positive control---But VFR, in accordance with the MPTS--Meaning that it can deviate from 3710's IFR flight to the "Max Extent Practicable." (mission requires VFR). And doing that is only going to minimize the services/separation provided by ATC (workload permitting under VFR flight following (positive control)).
In this case, you would still treat the TRSA like a Class C, but remain
under it's outer rings (VNAVS done at usually 1000' AGL max (usually below the outer rings of the TRSA).) This is until you penetrated the surface TRSA (innermost ring), which usually coincides with the Class D airspace around the airport that provides the TRSA. At this point in time, you'd be told to squawk a discrete code--which means you'd be "participating" in the TRSA in the spirit of the above quotes from 3710T.
Assuming they used your callsign when they gave you the squawk, there would be no need to be under "radar contact."
So, I agree and disagree all the same. It is, for all intensive purposes, a Class C with one major difference...A controller of a TRSA should never tell you to "remain clear until radar identified," which is something you'll usually hear in a Class C (hence the "Contact Approach 20NM out on 123.45" boxes all over the VFR sectionals.) Despite the squawk, the only requirement is 2-way radio comms in or out of the Class D airspace (usually overlapping the surface TRSA area...).
Now, if he says "aircraft/callsign, remain clear of CLASS D airspace..." than that's a whole 'nother question, but has nothing to do with the TRSA (of which we military types are required to participate IAW above clips from 3710T), it has to do with the TOWER controlling the airport. And therein lies the major difference.
Clear as mud?