If we're willing to spend even more to get better estimates, I have an idea. Let us consider creating an island where people can be offered a very stable neutral standard of living, and then look at the willingness of various people to move there.
Imagine for example an island held at 100AD Rome technology level and climate, divided into stable predictable small villages, with some variations possible in local island quality of life (such as via hours of work required or house sizes offered). These village need not be self-sufficient; the main goal is to maximize the predictability and stability of local quality of life from the view of potential immigrants, and to minimize the variations in these quality expectations due to the degree to which village life is "like" life from any particular immigrant's prior home.
Then random people and families from around the world could be asked for their cutoff island quality of life, the level they would require to move to the island. If this quality was less than a previously randomly generated quality offer, they would actually move to the island. These quality values could then be the data on which to base a better estimate of quality of life around the world and across time. To maximize the amount of this data, at perhaps some sacrifice in quality, one could ask larger groups for their cutoff value, but only actually make the pre-generated offers to a small random subset.
To avoid variations due to preferences for who else is in the village, one might strive for village populations to be roughly random samples from across the globe. Thus offer levels should be adjusted per nations so that in practice most people from each nation will accept the offer. Offers should also be generous enough so that few people will actually want to leave the island soon after they arrive.
To minimize the dependence on the ability of local leaders or local innovation in village layout, etc. we might prefer stable non-local management in many villages.
I'm sure there are lots more complications to consider, but overall I still think the idea is worth considering. Biases in estimates from this approach can be large and still be substantially better than existing estimates.