The two problems are totally different as well as the solutions.
Not necessarily. It depends on how the noise is coupled to the audio circuity. My suspicion is that the noise is riding on DL's internal audio ground bus. If you use an unbalanced connector that shorts ground to cold, which is exactly what happens in a 1/4" TRS connector when you plug in a TS cable, noise riding on the ground would then be introduced to the cold input on a differentially balanced input. Since the noise would not be common mode on the hot connection, it would not cancel. In the case of plugging in the unbalanced cable on on the input, the noise would be introduced into the the DL's channel input as opposed to the self powered monitor scenario where the noise would not be cancelled at the monitor's input using an unbalanced cable. In both cases though, the source of the noise would be the DL's signal ground bus. When using a balanced cable in both instances, the cold connection is never tied to ground and the non-common mode noise would not be injected into the balanced input though the noise would still be coupled to the upstream or downstream device's audio ground. So long as said device has proper isolation to prevent that noise from coupling within it's circuitry, you wouldn't know it's there. Of course, this is just a theory, but it seems logical based on reports. At my day job, we design a variety of FPGA based digital A/V equipment and go through great pains to ensure that switching PSU noise and various digital clock circuits don't get into the analog audio circuity. It's not always easy & I suspect Mackie didn't do their due diligence in that regard. FWIW, this isn't the first time I've noticed a whine in Mackie digital mixers. Their d8b board also had a whine on the control room outputs of a similar nature, though it may not have been as bad.
As for line level transformer isolation, I agree that the Jensens are the way to go if you can afford it. In lieu of those, I'd recommend the Whirlwind ISO1 or ISO2 transformers for line levels as they have very good specs for a lot less money. They can take fairly hot signals (+20dBu @ 20Hz) without saturating and are pretty flat to that point. The devices come with both 1/4" and XLR connectors on inputs and outputs so you can balance and unbalanced lines as needed along with the isolation.
And to the OP, get a decent quality passive DI for the keys and be done with it. As long as the transformers are good, it will sound great and you won't have to worry about noise problems. I generally use Radial JDIs for keys and other line level devices. They have Jensen transformers in them and sound great. If you can't afford the JDI, the Whirlwind Directors work ok.