If I'm currently doing my first postdoc in the US on an F1 OPT (in Astronomy) and I decide to apply for either an EB1A or an EB2, I understand that it would show my intent to immigrate making me ineligible for a J1 visa. Because of this, any future postdoc position would need to sponsor me for an H1B visa (assuming that my EB1A was denied or my EB2 has a really long wait time). Given this, will this reduce my chances of getting a second or third postdoc with a university because they'll have to sponsor me for an H1B as opposed to a J1?
P.S. Here are some examples of universities that state that they will sponsor an H1B for a postdoc if they have a pending green card application with USCIS: https://research.upenn.edu/postdocs-and-students/postdocs-foreign-nationals/ and https://postdocs.stanford.edu/postdoc-admins/how-quick-links/request-visas-postdoctoral-scholars