I think this is true for english-speaking countries, but less so for most european countries. In Switzerland for example, you have direct access to 12 EA-aligned tax-deductible charities through Effektiv-Spenden (6 GH&W, 2 FAW, 4 Climate change).
GWWC on the other hand enables direct tax-deductible donations to 50+ funds & nonprofits across all main cause areas for the US, UK, Australia (& the Netherlands).

Has anyone thought about donation swaps for tax-deductible giving (a bit like kidney paired donations)? I feel like a good amount of people would be excited about giving to nonprofits that fall outside of the typical options (eg. LEEP or SWP instead of Givewell or THL), but end up defaulting to the latter because that's the only way for them to make tax-deductible donations to EA-aligned charities in their country. 
I would be excited about a mechanism allowing me to make tax-deductible donations to a charity of choice for someone in my country, who would in turn do the same to my preferred charity in their country.

Is there something like that already? If not, happy to chat with others who want to explore this further!

Is there evidence on the effects of extreme claims on moral circle expansion? 

I am relatively aware of the potential benefits (eg. talking about shrimp sentience might encourage people to start reflecting on the welfare of farm animals more broadly).
But it feels like there is also a potential failure mode with this current approach, where talking about extremely non-mainstream ideas such as stopping boiling vegetables or refraining from using antibacterial deodorant (as per the article) might make readers less likely to engage with similar arguments in the future.

Curious to hear if anyone has more insights on that!

Charity entrepreneurship has led a pilot project somewhat related to your point (2). There's more info in their writeup. 

One thing to keep in mind with PF doing "ineffective"grants is that they're sometimes limited by their statutes, eg. the Hans-Wilsdorf foundation, despite moving multiple hundreds of millions of $, can only do so in the canton of Geneva because the founder decided so when creating the org.