I never cared enough to test it but apparently some sources are designed with the balanced output in mind, which means their circuit has more or better components and therefore should sound better; the single-ended is an afterthought and is there for convenience. Your DAP could be one of these sources.

per hifigo (this generally apply to most eartips): > Narrow bore Ear tips tend to increase the lower end presence, producing a powerful bass response. They bring a slight cut down on treble extensions too. When you use Wide Bore Ear Tips, they bring out the treble energy of the IEMs, the soundstage is also wider and spacious. The wide bore Ear Tips also add a bit of brightness to the IEMs.

perhaps you could try using tips that include filters. Azla Max (silicone) and Comply (foam) are the ones i know of.