Conservation reject--is there hope

No. If the coin was rejected then the TPG made the tough decision to not take your money for something that couldn't be fixed.
Lance.

are you wanting to get a problem coin into a non problem coin holder here?
or
are you trying to conserve a coin here for sake of conserving it here?

there are services for the last one
google coin repair services if you are trying to conserve a coin for sake of conserving it

Depends on the coin. I have had some luck with early copper that was rejected by the conservation services. It usually involved
soaking the coin for a month (or more) in an olive oil/secret ingredient solution, then gently removing the encrustations that had
loosened. PCGS and NGC will not spend that kind of time on any coin, so I certainly do not blame them for the rejection.

On the other hand, silver coins that have been etched by PVC contamination are usually goners. I made one Morgan dollar more
visually acceptable by carrying it around in my pocket for a while, slowly circulating it down a grade and smoothing out the roughness,
but many here would consider that a bit extreme (my wife certainly did, especially when she would fish it out of a pocket when doing
the laundry). We compromised -- now I do the laundry whenever I have a "project."

It all depends on the amount of time you are willing to invest, and how close to becoming a coin doctor you are OK with.