Though I have an impedience matching XLR to 1/4-inch adapter, it has always resulted in significantly reduced signal strength from my mics when using them with the PSR series. When I switched to a direct adapter cable, I had normal signal strengths, no distortion and excellent results.
Give the adapter a try--it cannot damage anything, and it may solve some of your problems.
Good Luck,
Gary
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PSR-S950, TC Helicon Harmony-M, Digitech VR, Samson Q7, Sennheiser E855, Custom Console, and lots of other silly stuff!
K+E=W (Knowledge Plus Experience = Wisdom.)