Since the problem seems to appear when you use the 1/4 track head it could possibly be the alignment of the 1/4 track head that is affecting the sound. IME 1/4 track heads are often fairly touchy to get just right. Unfortunately there aren't many 1/4 track alignment tapes around. We align visually with clear tape, then take a first cut with a two track tape, and then Shawn and I usually throw on a 1/4 track tape of music we know really well to do the final touch up on alignment. Being off just a little bit laterally can throw the frequency response off quite a bit - it might lose bass, it might lose treble, you can also hear the stereo image get better and worse. You might want to try listening with headphones when you touch up the alignment this way. Go slow, and pay special attention to how much you turn each screw so you can return it to where you started if it doesn't improve things, before you turn the next screw.
Now I will say the IME it's usually the top end that goes first when alignment is off rather than the bottom end, but it won't hurt anything to try this and see if it makes a difference.
Once you have established that the 1/4 track alignment is optimal we can dig a little deeper, if necessary.