I think the most viable solution, one that is not a rework of several core systems of the game (which seems unlikely at this point), is the addition of trade posts in foreign provinces. A country can, though an expansion idea group perk, in any other-continent trade company region, establish a trade post in a foreign or uncolonized province. It would additionally have to be within colonial range (trade range?). This would cost some combination of diplomatic power and cash. This would essentially give the trade power to the trading country, probably with positive modifiers. The province I could see Portugal having a large boost to trade posts efficiency in their ideas. The owner would get a boost to goods produced to compensate. Simple as that.
I'd additionally suggest showing trade posts to count as part of a trade company, potentially giving you merchants. It would also give colonial range and trade range, allowing you to go far without actually owning any provinces. You'd also gain a cb on the owner country.
While not strong enough to be the basis for your strategy, it could make up for this in its ease of use. If implemented properly, it could work. With some alterations and additions of course. The ideal would be for it to require a decently strong navy (at least to have more than a few posts), while also ensuring you can't go entirely wild with them. I think this could be extended to work for merchant republics, though then also at the home continent. These new trading posts would have a better name to avoid confusing them with the old ones for the merchant republics.
There'd also have to a possibility for war when the owner refuses the Europeans. This would be a new casus belli, where the "defender" (owner of the posts) would have the wargoal to blockade or occupy coastal provinces. (I think this existed before?). In addition, there would be a diplomatic action similar to "demand province", just without the aggressive expansion.
This is good stuff. Pay money and/or mana to establish a trade post in a foreign asian or african province(i'd limit it to owned provinces), you get all the trade power, province gets a large bonus to goods produced. Say, you need positive relations and completed expansion ideas to do it. Only one nation can have a trade post per province.
You can also add an upgrade chain to trade post, say rank 1 (default) extends trade and naval supply range, rank 2 extends colonial range, rank 3 allows you to build manufactory for the AI, fabricate claims and hire mercs, rank 4 would give you a permanent claim on the province and fire(or enable one with a reasonable MTTH) an event for the AI where they either cede the province or kick you out, giving you a good CB. Unlock the ranks with each age, pay money/mana to upgrade. Every rank also increases the trade power you get and the goods produced the ai gets.
I'd also love it if you actively had to use ships to setup and upgrade the trade posts.