Secondary or at racking time would be my choice.
Primarily the hops are my concern. I'm presuming you'll want citrus types such as Amarillo or maybe even Sorachi Ace?
I was thinking of using either citra/amarillo and sorachi ace,14g/5gal at 10min and knockout.
I probably will layer the jasmine and green tea by late WP additions and dry hopping. Just not sure on the amounts and when.
Check the ph of hot green tea and if it's in the realm for a mash. If it's okay try it as your brewing liquor. Adjust the ph if slightly off. Some green teas can have a delicate flavor. Others stronger. I call it "seaweedy." Might as well eat a sheet of Nori.
Another idea would be to make a couple of pots of green tea, reduce it all down to a pint to concentrate the flavor. If it tastes good use that with your priming sugar, or with out if you force carbonate.
I like your ideas Steve, my one concern is that boiling tea, like coffee, is not recommended because it extracts too many tannins. That being said, mash hopping and first wort hopping, are a similar concept and the opposite of expected result happens would great success. Boiling it down and reducing it I think may be a bad idea as it would concentrate these tannins. Could one make an extract with vodka and still retain the aromatics of the green tea and jasmine? Thanks for all the help guys!