But no one knows what the recovery will be if a credit event actually happens. People who reade high-yield names often keep track of their own physical recovery assumptions $R_A$$R_P$ different from the standard $R$ used for quotes, perhaps even having a term structure. This alternative assumption does not affect their market to market / upfront, though. They might do some calculations while keeping constant their mtm, such as hazard rates $h_p$ (having term structure) implied by their physical recovery assumptions $R_P$.
On very rare occasions the market participants agree to change the quoted recovery assumption for some name, e.g. from 40% to 25%. In this case they will aim not to minimize the mtm impact from this change, while allowing the risk neutral hazard rate to change significantly. I don't see any use in looking at different recovery assumptions while trting to keep the risk neutral hazard rate constant.
For calculating mid in order to mark to market, you'dyou could calculate the risk neutral hazard rates (or neutral default probabilities; but not upfront) from $S$ and $R$, and use the risk neutral hazard rates to back out the $R_A$ spread (or $R_A$ upfront) using $R_A$ recovery assumption. The ratio you cited is a rough approximation of the spread obtained by keeping the hazard rate constant, rather than upfront constant. Note that the upfront and mtm of a fixed-recovery contract will have much greater sensitivity to $R$ than that of the vanilla contract.
However I'm not sure if it makes sense to combine risk-neutral (used for quotes) and physical recovery assumptions like that. I'd be more comfortable if you had your own physical recovery assumption $R_P$, and keep constant the hazard rate $h_P$ implied by $R_P$, and then backed out spreads using alternative recovery assumption $R_P$
