What is your room like, and how is the Klipsch center channel oriented/mounted? Is it close to a wall, in a cabinet, on a dedicated speaker stand, etc?
The JBL-L300's are ported on the front and the Klipsch RC-64 is sealed (ie: non-ported), correct?
Yes But they are being cut off at 80 cps since they (having a box tune of 27 cps) result in a phase shift there, which interferes with my SVS sub which has a box frequency of 18 cps). If crossed over low it results in a big response

dip at about 25 cps. For info, since this photo had been taken I have put an SVS PC 13 Ultra inboard (to the right and behind) the left JBL. It replaced the SVS PC 12 seen to the Left of the JBL left speaker. The big JBL sub in the foreground is not in use because I have no good crossover for it and it is also about a 27 cps crossover so will not combine well with the SVS 13 ultra. In addition, the SVS does go much lower and with more power in the SVAS amp than My heath 200 watt amp bridged for the 18 inch JBL sub.
I had similar issues with center channel dialogue when I moved into my current house, and it was due to the built in cabinet in our living room. The center speaker is below the TV, on a shelf in a built in. Same with my RC 64 but it is sealed. The one I was using was rear ported, and it was causing issues due to the built in acting as a sort of band pass enclosure. I ended up replacing the speaker with a sealed unit and recently EQ'ed it with REW, and the dialogue is fantastic now.
The equipment you are using is MUCH better than anything I have, but what you're describing really sounds like the same thing I was experiencing, so it makes me wonder what your room is like and how the center channel is positioned.
Another thought is if there are any environmental effects going on. Could it be possible there's something else switching on and off causing frequencies to be impacted? Maybe an HVAC system, which when running, is causing your hearing to be effected? Considering your comment about the sound changing intermittently Usually the source changing scenes or a commercial. It is definitely affecting some part of the spectrum, not an equipment thing but a broadcast (or movie scene ) thing would lead me to wonder if there may be an outside influence impacting your perception of the audio in the room.
Also, at what levels are you listening? TV about 65 dB. movies, maybe 75 in dialogue areas. Hearing fatigue at moderate levels over time can really change how we hear certain frequencies as well. As an active musician: how the stage sounds when doing an initial sound check, and how it sounds after finishing a set, is very different just do to the time spent exposed to the levels. You should see what happens to your hearing while driving thru the Holland tunnel with the windows up taking my daughter to an audition. She warms up and really blasts. After a few minutes, I probably could not notice the sound if in a bell tower! She now sings with Pittsburgh Opera Chorus so I don't get much chance to get recordings anymore but I do have a lot of DAT and Nakamichi cassette masters of her as well as the McKeesport Symphony orchestra, several local choral groups and some Professional theater organ concerts I taped for the theater organ concert sponsor and performer. Also note our hearing is different in the morning than it is at night, etc ...