Well, now. In attempting to _earn _a Self-Referral today, I learned how to not earn one. 
Process: Clear cookies, paste Clean Link into browser URL bar, change name on custom Design, Add to Cart, log in, check out. I clear cookies before the first order and after each order. I do this b/c the Z system has been wonky on Referrals since the beginning of time. And I place orders on a second computer where I don’t do any other Zazzle work.
Order numbers below are for my reference. Third-party cookies and Java on/off are references to my browser settings for Zazzle on that machine. “New customize interface” refers to the new interface a customer may see now which I believe to be in A/B testing.
Order ID 131-41781193-1857009
Third-party cookies off > Java turned on in window (off by default) > new customize interface > no Referral
Order ID 131-50534084-3691429
Third-party cookies off > Java turned on in settings > new customize interface > no Referral
Order ID 131-29253922-7487801
Third-party cookies off > Java on in settings > old customize interface > no Referral
Order ID 131-15173342-8667631
Third party cookies on > Java on in settings > new customize interface > no Referral
On my last attempt, Order ID 131-24178869-5605323 , I turned off four Chrome Browser Extensions:
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UBlock Origin
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User-Agent Spoofer
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All Fingerprint Defender
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Fingerprint Spoofer
And once turned off, I earned the Referral (old interface).
So if you’re working closely with a friend or relative or even a customer where you’re comfortable saying “The site might not work as intended, if you have blocking-type extensions enabled in your browser; you might turn those off, place your order, and then turn them back on,” that might help your Referral game. Nowhere in such a statement are there any untruths – the site is intended for us to earn Referrals. 
IMPORTANT ETA: I just noticed that the Discount Code didn’t auto apply on the first four orders! THAT would be a motivating factor to someone making a purchase!
Congrats on the sale!