My method:
I calculate "expected" PO,A,ER,DP for each player
I take park adjusted DER into account
I do adjust for %LHP, %GR/FB and runners on
For range I use 50% RF(Adjusted) and 50% ZR

I subtract these expectations from the real stats
I multiply these "deltas" by "run values" for each statistic. This gives me a "runs saved" statistic.

The run values for plays might be a bit mild to prevent the numbers from going bonkers.

I do not give credit for OFs holding runners.
I do not give credit until year end for 1Bs who prevent 3b,ss and 2b throwing errors.
I am working on a method to estimate the number of 31s, 36s and 363s that a 1B like JT Snow might start.

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More detail
To credit for range I average two things:
1) The extra plays make by fielders compared to what would be expected considering the environment. I also factor in team DER here.
2) Zone rating.

An example:
Eric Chavez 
724 ZR 
3.21 Range factor
95 nZ (ZR/average zone rating of 760)
127 nRF (plays/expected plays given environment) 
+2 runs saved due to range

I credit Chavez with above average range because his (nRF+nZ)/2 is above 100. It is possible that the scorer in Oakland is being too tough on him

Sheffield is the opposite of Chavez. He has a good ZR but he is making fewer outs than expected given his playing time