One easy trick that hasn't been mentioned yet - naval countries in Asia can simply invade Africa.
Attack Mutapa or any other pagans with the free CB, and wait for the provinces to core to extend your colonial range, or get the first Westernisation step off fast-teching Muslims like Oman. Then, if the Iberians have invaded the Maghreb or the sub-Saharan region, start a colony next to their territory - it doesn't need to be fully complete. Better yet, if Europeans are at war with the countries there, just declare war as well and take the chance to grab one province from the locals.
Once you've fully Westernised, the province can simply be sold to avoid wars. But if you have a big enough navy you can just take it on the chin and let them DoW you, and watch them dash their fleets against your wooden wall.
As unified Japan, I ran up against Burgundy, the Papal States, and GB (in the 1500s!) on the west coast of Africa, which I had seized from Animist Songhai. I gave Burgundy and the Papal States military access, but GB refused and DoWed me - bad idea, as I proceeded to blockade their entire island with my huge fleet, so much for rule Britannia! The only time I felt caught out by the Europeans was when I took the -6 stab from military modernisation, and both Burgundy and the Papal States declared Holy War at the same time. Burgundy took -5 stab and a (ineffectual) blockade for their troubles, while the Papal States, despite being clever enough to cancel military access, peaced out quickly. I hate to imagine what might have happened if both of them had taken the war all the way as their combined navies were larger than mine.