I had a similar experience with one of my JVC M70s. One would play the tape correctly but the another one absolutely refused to play the same cassette. Ended up when I compared the two boxes, that the one that played correctly seemed to have more lift on the metal support tab at the bottom of the player and on the tiny metal spring tabs on the cassette door. Someone, at some point, slightly bent them. That ended up resolving the issue.
My point here is to try the cassette that is struggling in another player to determine if it indeed is the cassette. If the cassette drags in other machines, then you can be for certain its the cassette rather than the machine just not liking it. Also, do not apply lubricants to the tape itself. Most of the time a tape drags for four main reasons.
1: Warped case. Sometimes I have had instant results by transferring the tape to another shell.
2: Reels that can warp and drag. Again, you can transfer the tape over onto a different reel from another cassette.
3: Stuck tape from heat, moisture and/or mold - Rewind and FF usually corrects this but playback may cause build up on roller and head.
4: Tape stretch. This is the worst thing ever because you can't do anything about it. Once the tape is stretched, its gone.