Just a thought ... What do they use as the customer id going into Target? Best case scenario would be to surface some sort of customer id in the client side (from server) once phone number or email is known and store that as a cookie or local storage (if only using one subdomain). Then you could use that cookie value as the mbox3rdpartyid. If not, then you would have to collect the out of the box TNT id that gets generated on the Target end and comes back in the mbox cookie. With either approach, you could update the Target profile server side with the values that are non PII.
https://developers.adobetarget.com/api/#updating-profiles