Theoretically one could try to take an Thanos-like approach with equal mass-murder. Unfortunately that wouldn't really help, since most countries can't afford to lose half of their population, without going into a severe crisis-state. Instead we could just eradicate whole countries, not based on citizenship, but people who work in or profit from this country (to include Billionaires who get their money from companies in these countries). Chance of eradication correlate with the number of people to be eradicated (so a country with 1 Billion people in a world with 8 Billion will have a chamce of 1/8). Like that we could sit back and spin the wheel of fortune - "Death Edition" - till we get past wanted population size.

This would also solve the issues steming from capital you mentioned. Due to globalisation the likely collapsing of China, India, maybe the USA, 1-3 big European countries and a hella lot of of Asian, latin American and African countries providing various resources, the economy and the finance systems would likely crash. Industrial states will probably have the most problems getting back on track due to their dependency on foreign slave labor. This rebuild may again be very eco-damaging, but with enough pressure it could be sustainable. For the finance system, there is the question if we even want to reestablish this system, where all debt can never be fully paid back or there is a trade with derivatives. (Seriously it's fucked up. In 2007 the trade with derivates was about 1 Quadrillion, while the products produced in the last 1000 years roughly equal to 100 Trillions, a tenth. Guess what a major factor of the 2008 financial crisis was.)

For not-so industrial countries, it would maybe not be that bad (?). While not having the ability to buy first world products, there also wouldn't be assholes using them as a trash depot, or selling them stuff to bad for Europe and the USA at so cheap prices that the local economies collapse. But economic rise would in these countries probably cause more damage to the enviroment, due to missing knowledge and technology of e.g. sustainable energy.

But at least it would be indiscrimatory (as much as you can be in an genocide without trowing humanity back into medivial times).