Are funds (such as the Long-Term Future Fund) willing to give extra money to AI safety researchers to balance for the opportunity cost of taking an "industry" job?

I think you can guess a reasonable answer even as a complete outsider (like me), considering the purpose of these funds, which is to maximize the amount of expected good they cause by the allocation of their money. A few things that must come into consideration:

1. is it productive to pay very good researchers the bare minimum they need to survive? No:
   • it consequently make the path of independent research unattractive to most;
   • it produces some level of adverse selection in future applicants, i.e. you'll move toward getting more applications from people who couldn't really be hired in the industry, which isn't always bad but could be thought to correlate with not being an excellent researcher;
   • you don't want your researchers to waste too much time and energy on things that could be straightforwardly solved with a bit more money.
2. on the other hand, paying too much has a few issues:
   • the money spent on a researcher hitting decreasing returns after a certain point;
   • also some level of adverse selection, if people know they can make the same amount of money here or in the industry, and your fund's approval process is lighter than industry interviews due to a lack of resources and a hits-based giving approach: you might get an influx of candidates who aren't altruistically motivated and were rejected from the industry for perhaps good reasons;
   • damaging the reputation of the movement by appearing to allocate your money frivolously.

In terms of existing data, you can have a look at past public payouts, for example the December 2021 LTFF report [EA · GW]. In it, you'll find a 6-month salary of $50,000 for a well-known independent researcher, which is above the bare minimum needed to survive, probably allowing for some level of travel and luxury, while staying well below industry standards.