The Matsumae will probably offer the Thule the same stuff they offered the Ainu, laquerware, rice, sake, wooden utensils, gold and silver jewlery, and *iron cookpots*. Here's another source for sophisticated metallurgy to enter the Thule sphere, as a source for reverse-engineering if nothing else.
Desire is hardly the problem. The record for indigenous cultures was a near insatiable demand for sophisticated products of Western or Japanese culture.
Let me put it this way: Until you've tried to cook a stew by digging a hole, lining it with the skin of your kill, filling it with meat, plants and water, and then heating rocks in a fire and dropping the rocks heated from a nearby fire in.... you will not appreciate the godsend that is an iron cookpot. Even such simple things as twine and rope are wonderfully valuable.
It's harder to talk about what the Japanese traders have to gain from this relationship. OTL Matsumae exports to mainland Japan were mostly bulk foodstuffs (fish) and fur.
Bulk stuff is expensive to transport, especially relatively low value materials, relatively large distances. The Matsumae purchases OTL wouldn't be sufficiently valuable enough to go much past Hokkaido. You couldn't make a profit bringing that stuff down from Kamchatka. And there'd be no need to go to Kamchatka, because the local production in Hokkaido would be entirely sufficient anyway.
There was some specialist trade in falcons,
There's always a minor trade in exotic critters. It seldom amounts to much. Not unless you're running a Roman Colosseum.
but little attention was given to ivory or metals....or guns.
Well, metals are a tricky thing. You have to mine them, either transport the ore home, or smelt it on site. It's extremely expensive. Generally, only gold or silver offer the hope of a return. The big problem is finding a valuable deposit.... that's usually more luck than anything.
You'll recall during arctic exploration, there was an expedition that thought they found gold, came back a few years later with a gold mining fleet, and lost their shirt. That kind of prospecting is 99.9999 per cent of the time a dead end.
I pick Ivory as the gateway trade item for a few reasons.
1) Historical precedent - Walrus ivory was one of the key trade goods for the Greenland colony and one of the economic backbones of its export economy. The loss of the Ivory market to Africa was one of the death knells for Greenland. Ivory was also a huge African export, once those trade routes opened up. Historically, Ivory has been an a rare, high value commodity.
2) Ivory is really portable. It doesn't rot, it doesn't decay, it stores indefinitely, it's very easy to transport, can be divided or subdivided with little loss. It's much easier to handle than roseroot or furs or other items.
3) There actually does seem to be some contemporaneous artistic and artisanal tradition within Japan at the time that made use of the small quantities of Ivory that they obtained. In short, it's a trade good for which there may be a pre-existing potential demand waiting in the Japanese culture. Ivory may be something that they'll just pick up and run with.
4) Ivory in the 19th century became a huge and valuable import item for Japan, so we're not unreasonable in possibly backdating it as an artisanal good. This to my mind reinforces item (2).
5) Ivory is a non-renewable resource which has an interesting consumption/acquisition profile. Okay, look - you go out to the Aleutians, Ivory is all over the place, its a potentially valuable good, and there's tons of it. You harvest the walruses, you trade with the natives you go home and make a ton of money. But then, you go back out - the walruses are all harvested, or at least the ones that they were willing to let you harvest, and the natives have already traded all the cheap ivory they're willing to let you have... so now it's expensive and difficult. Unless you go out to the next Island.... and the next.... and further up the coast... and further... So, it's a valuable commodity which can maintain a continuous, even an expanding supply over a long period.... but to maintain that continuous/expanding supply, you have to go further and further and further every year, or every few years.
So essentially, it is quite possible to establish a stable ivory market, and to meet the demand of that market, and even a growing demand, in a relatively continuous even fashion, that would take Japanese sailors eventually far into the Thule realms, with a reasonable prospect of guaranteed profit. Because the profit is guaranteed with a relatively small but very durable cargo, it also allows the sailors and merchants to experiment with other commodities which might be valuable.
This would be where you'd start to see people coming back home, with 'risky' cargos like Roseroot, Walrus Hide, Sealskin, Otter fur, or other Thule goods - you have the luxury of taking a chance and maybe selling some of this other stuff. These secondary goods, if they find a market, then become part of the trading network. Indeed, some of them may supplant Ivory, or at least rival it in importance. Ivory trade becomes the cutting edge that opens up things like Roseroot as a significant and perhaps dominant export.
