I seem to hold the uncommon view that both feminism and the teachings of most PUA types are compatible and good things

I agree that there is compatibility between pickup and feminism that is under-explored.

Both PUAs and feminists are heavily focused on the same thing: the needs and preferences of women, and how men can fulfill them. The amount of time and effort PUAs spend trying to figure out and cater to women's sexual desires is crazy. Furthermore, they often consciously make a choice to develop aspects of their personalities and identities that they know will be attractive to women.

Yet PUAs differ from feminists in their views of what women's preferences actually are. PUAs assess female criteria from what women respond to, which may not be the same as stated female criteria. Also, even though PUAs attempt to fulfill a subset of women's desires, they are not always trying to fulfill all of women's desires all the time.

Both PUAs and feminists make some errors in assessing female preferences, but feminists are more wrong: I would give PUAs a B+ and feminists an F (see this and this for some research on female preferences). (On average, feminist women differ from typical straight women. For instance, feminists are probably more likely to have gender atypical gender expression and values, so it's not a stretch to think that they might have gender atypical preferences also. As a result, feminists, particularly feminists who criticize pickup, may be out of touch with typical straight women, and fail to recognize how the aggregate preferences of their sisters are incentivizing the very male behavior that they condemn. I've seen some feminists admit that they are attracted to traditionally masculine or dominant behavior in men, but I've never seen them also think through the implications of their preferences and the incentive structure that they enforce on males.)

Contrary to the guess in your post that PUA culture might include beliefs that men are owed more sex, my impression is that PUAs want women to have sex with them not because of a feeling of obligation, but because they have fulfilled female criteria for having sex.

Some PUAs believe that they "deserve" sex in general, but what they seem to mean is that they are "worthy" of sex, not that they deserve to have sex with any particular women. Other PUAs explicitly disavow the idea that they deserve anything:

No one deserves to get laid, and that includes you and me. But you can get laid if you work at it.

...

Though you are entitled, as a man, to do whatever you want and try to get laid with the women you wnat, you are not entitled to do it without effort. That's his point. gotta put in the effort, not expect to just happen like some spoiled kid

The whole approach of seduction, as I understand it, is to raise the chance of women wanting to have sex with you for reason of being attracted to you and comfortable having sex with you. PUAs want women to want them.

This approach is not only more ethical than (a) trying to get consent to sex by bypassing women's sexual and emotional preferences (e.g. obligation, prostitution), or (b) trying to coerce women into have sex without consent... it also wins way more and sounds rather feminist!