Upvote:4
As a visitor to the US, even as a US citizen, I believe your exemption is $100, not $800. But questions about how you should be classified based on your residence abroad belong more on Expatriates than here. The actual questions you've asked here, however, do not appear to me to be off topic:
How should I document my things, both used (personal effects) belonging to my wife and myself, and our new things to meet CBP requirements?
Make an itemized list of everything that will be remaining in the US, along with its value. Bring that with you when you travel, and present it with your customs declaration at the passport control desk. Don't use an automated passport control kiosk if you can avoid it.
The way it's supposed to work is that you tell them about everything that's remaining in the US, and they tell you whether you have to pay duty.
will CBP allow [my wife's] wedding clothes to still be considered my personal effects if sheβs not there?
I think not. The definition of personal effects includes the phrase "articles intended and appropriate for the personal use of the nonresident while traveling."
Should I carry some evidence of our marriage?
It shouldn't be necessary. It's seriously unlikely that a customs officer would challenge your ownership of the dress. But it's possible, of course, and evidence of your marriage can't hurt. A copy of your marriage certificate would surely be sufficient.