Sorry, I don't think I have relevant expertise to assess such empirical claims (which is why I focus more on hypotheticals).

Note many do not engage with my empirical claims about effects on soil animals for philosophical reasons ("that assumes utilitarianism!"), and assessing these is a comparative advantage you have. Moreover, in the effective altruism community, some people initially concluded that targeting farmed animals increases animal welfare very cost-effectively based on classical utilitarian reasons, and I expect many of those people to depart from classical utilitarianism after realising it plus empirical evidence point towards prioritising soil animals much more than farmed animals. People with a scout mindset, and not invested in any particular way of increasing animal welfare could be in a better place to assess the extent to which such departures from classical utilitarianism are post hoc justifications, eventually in the form of empirical arguments which are seldomly investigated.

As a concrete example of philosophical arguments being important, @Wladimir J. Alonso, the founder and innovation director of the Welfare Footprint Institute (WFI), values averting intense suffering more than is justified by its intensity. Some people, not necessarily Wladimir, endorse this so much that they would prefer averting 1 h of excruciating pain over an infinite amount of annoying pain, and would never consider effects on soil animals given other animals can experience much more intense suffering.

I suspect you are overestimating the difficulty of checking the empirical claims. I am pretty confident that funding HIPF decreases the suffering of soil animals much more cost-effectively than cage-free corporate campaigns decrease the suffering of chickens. I estimate HIPF decreases 5.07 billion soil-animal-years per $, and that cage-free corporate campaigns improve 10.8 chicken-years per $. For HIPF to decrease the suffering of soil animals less cost-effectively than cage-free corporate campaigns decrease the suffering of chickens, the reduction in suffering due to improving 1 chicken-year would have to be larger than than from decreasing 469 M soil-animal-years (= 5.07*10^9/10.8), whereas I calculate chickens only have 921 k (= 221*10^6/240) times as many neurons as nematodes, which are the soil animals with the fewest neurons. Moreover, I think the number of neurons underestimates the absolute value of the welfare per animal-year. Rethink Priorities' (RP) moral weight project assumes shrimps have 10^-6 as many neurons as humans (see Table 5 here), but the estimate for their welfare range in Table 8.6 of Bob Fischer's book is 8 % that of humans.

For the reasons above, I am also pretty confident that funding HIPF changes the welfare of soil animals much more cost-effectively than cage-free corporate campaigns increase the welfare of chickens. However, I am very uncertain about whether HIPF increases or decreases animal welfare due to being very uncertain about whether soil nematodes have positive or negative lives.

To clarify, I believe researching whether soil nematodes have positive or negative lives would increase animal welfare even more cost-effectively than funding HIPF, but that this still increases animal welfare much more cost-effectively than interventions targeting farmed animals.

I would prefer saving human lives to decrease animal welfare such that soil animals had positive lives. I think saving human lives decreases soil-animal-years, and therefore increases/decreases the welfare of soil animals if these have negative/positive lives. I guess they have negative lives, although I am very uncertain, and estimate the welfare of soil ants, termites, springtails, mites, and nematodes is -977 k times that of humans for my preferred way of comparing welfare across species.