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I would optimize my EMSA in the only way possible by varying the salt concentration of KCl, and the pH and conducting EMSA to see the results of the shift (the more shift the better with everything else the same - volume and amount of RNA / protein).
You can also look at the buffer - HEPES vs other buffers.
Timing most will find will not have a bit difference, and binding temperature usually is the same for most proteins. If you look at most papers they inhibit RNAses and then incubate at 37 degrees for a short period (5-15 minutes or more) unless you get degradation (then do it at 4 degrees C for longer binding times).
UV crosslinking is usually done on ice.
Please upload your EMSA optimization so we can help.