I was able to solve my noise issue by low passing the output of the Seed before it reached my output buffer, per a suggestion from another user. Hope this helps someone else!
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Could you please provide some more details on the transformer/circuit?
Specific questions:
Is it a 1:1 isolation transformer or something else?
Manufacturer/part number?
I may have spoke too soon! (TLDR: I think the transformer was a red herring. But I did find some other interesting details on the symptom.)
After doing more investigation, there seems to be more variables at play in my situation to be useful to others. What I’m finding is that with my audio interface, the noise only occurs if the input gain connected to the Daisy is above a certain point. If I keep each channel gain right below that point, but then compensate with the master gain of the interface, I can juice the usable signal seemingly indefinitely without running into the noise. I’m not sure how to dig further into the implications of this, but it does seem to me like another case of the noise being dependent on the characteristics of whatever is connected immediately after to the Daisy.
As far as the transformer goes, I originally just grabbed a transformer I had laying around from a friend’s record player, so no part number and I don’t know the ratio. Likely a step down ratio, which probably masked the issue in my case because I had to apply makeup gain on my interface. I later tried with a 1:1 EI19 transformer and it actually made the noise worse! So… nevermind on that angle I think. 
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Thanks @jackcampbell and @AsaLPatterson - this is getting curiouser and curiouser!
I was trying to figure out how important the matching of those 1 Meg-ohm resistors is in the low pass filter op-amp circuit above, and found this page on low pass and high pass filters useful, so adding it to the trail:
And there is a lot of generally interesting info at the main page: