Looking for Indiana Jones-esque RPGs, books, media

[Jhaelen]

Gumshoe seems like it might be a good fit, customizing for archeology just like it was customized for Trail of Cthulhu.

Yep, imho Trail of Cthulhu would be an excellent fit. By default the rules support two modes of play:

Pulp (for the “desperate action” feel of Robert E. Howard or Indiana Jones) and Purist (full of philosophical horror and cosmic dread)

(emphasis mine)
E.g. Stunning Eldritch Tales is a collection of four short adventure modules using the Pulp style.