Possible cause of harsh mids?

pk, I just had another thought. The Exact cartridge has an extraordinarily high output, 7 mV! It may be overloading your phono stage. Here is the inexpensive way to figure it out and fix the problem. Go to Digi-Key and get a few of these, https://www.digikey.com/en/products/detail/stackpole-electronics-inc/RNF14FTD2R00/1974192
They are very high quality metal film resistors, 2 ohms. They will cut the voltage in 1/2 to 3.5. I would insert them right at the cartridge. Cut the resistor leads short, solder a cartridge clip to one lead solder the other lead to the red tonearm lead then cover the construct with red heat shrink. Do exactly the same to the white wire. The resistors are like 15 cents a piece!  If it does not work just return everything back to stock. If it works and sounds fine you have fixed the problem! If you decide to try this let us know what happens please. Another way to get an idea if this is the problem is take the record somewhere where you can hear it on another system and see if it distorts in exactly the same place. If it does then it is the record, if not then it is your system and the cartridge overloading the phono stage is an excellent candidate for the prize.

One note on sibilance. Lowrider is right. It is unusual to get sibilance in a recording, it happens but it is rare. Sibilance, in my experience is a product of the system and or room. Sound between 3 and 4 kHz has a lot of energy and can bounce around a room for a relatively long period. Then our ears are more sensitive right at these frequencies, a perfect storm. If anything is prominent at these frequencies you will get sibilance particularly with female voices and violins both capable of broadcasting a lot of energy in this area. The BBC developed the Gundry Dip for this problem and many loudspeaker designers will intentionally cut a few dB out of this region to make their speakers sound smoother. My buddies Watt/Puppies do this. 

Yes Audioguy85, Back in the 80's commercial pressings were hit and miss but the static and other noise was not associated with peaks in the music. It was random. I had several Columbia discs that actually had little bubbles in the PVC with some of them open to the surface. There was a Warner album with something in the PVC, sounded like sand. I always took them back and got replacements. Sometimes the defect is in the stamper and you get exactly the same noise in every copy you get as the store usually gets a batch of consecutive discs off the same stamper. There was some great music on these labels and like you said, sometimes you just have to live with it....until you get a digital copy of the record:-)

Static like distortion and sibilance are two entirely different things. If the OP had heard this on other records he would have reported it. If his phono stage were overloading it would also do it on other records. I would tend to believe the OP and that it is a unique problem with this record, which means it is a problem with the record. If it walks like a duck and talks like a duck, it is usually a duck. In millercarbon's world it becomes an ostrich.  

It was probably played on a turntable that could not track those peaks consequently they got knocked off so to speak and you hear distortion. This is assuming your table is tracking correctly. 
If you like that record get RTF's Romantic Warrior. This will really blow you away. Records like the Leprechaun, Friends and My Spanish Heart were done in the years following RTF when Chick was trying to find a new rhythm. I wish he had veered more towards classical jazz. IMHO these interim records were a bit...cheesy. (I have them all) Polydor and Columbia pressings at the time were not the best.