I guess I don't have the same reservations on using linkedin. You can of course omit information as you like on linkedin, same as you would on your resume. I do not make posts on Linkedin, but try to keep the resume type info more or less up to date.
The info I put on Linkedin, I'm comfortable being publicly available. Linkedin does block anonymous viewers, but you can't see everyone who views your profile without some premium subscription. But it IS possible. So slightly better than just hosting a resume on a public site.
If you're not willing to post the information publicly, then I think you just have to put in more work, find places you want to apply to, and directly send them your resume. But it just won't really be possible for people to discover you on their own.