Warped?

Are your saddles bottomed out? If so, from the looks of things 'super tweakage' can't be avoided. It looks to me like you need a shim. That doesn't void the warranty.

 

A neck shim is pretty simple to do. Get a business card, loosen the strings and remove the neck. place a portion of the card at the base of the heel and cut off that portion of the card that covers any holes. While you have the neck off make sure the screws slide through the body freely; if they don't use a file or drill to make the holes in the body big enough for the screws to do that. Reattach the neck and tighten the strings until almost in tune, now make sure the strings are centered on the neck. If they are off to one side loosen the screws some and center the neck so the strings are in the right place and retighten the neck. Now, tune the strings and see how the action is. How did your strings go from hitting the pickups to a centimeter high in a week?

 

Yep, usually. In extreme cases you might need two layers, but try it with one first. You are dealing with ratios here specifically a 6:1 ratio is this case,

 

It's not unusual that a brand new bass comes to the user in that condition. Sad but too often happens. But, I do have a big issue with the seller demanding another $50 to "repair" it. What other item can you think of that you buy new and have to have it repaired immediately before it is useable. We're not talking "adjustment" here - the owner has adjusted it as far as it will go. We are talking about repair. Bad on the manufacturer and the seller alike.

 

Put that measure immediately behind the string so it is resting on the fret. Repost. Holy crap no wonder you have 10 mm of string height!
Where is it buzzing?

 

When you measure the string height you are measuring from the top of the fret to the bottom of the string. so the marks for mm should be placed on the fret. No the intonation screw will change the fret tuning, you are attempting to eliminate a buzz. How far up the neck does the buzz go all the way; or does it stop somewhere?

 

Don't do that. 3 mm at the 19th isn't bad. For an Affinity, I think that's pretty good.And NO do not move the truss rod. The truss rod has no effect that high on the neck.