House Haillenarte also seems to be open to employing foreigners, even before the end of Heavensward.
Most prominently (though not so useful for indicating the overall stance of the house) Stephanivien hired a Lominsan to work for the machinists' guild as marksmanship instructor.
Some
levequest descriptions indicate that there is an Ul'dahn pugilist training knights "as part of a military arts exchange facilitated by House Haillenarte".
And they are also in charge of the Diadem, which is (more-or-less theoretically at this point) specifically recruiting adventurers post-Heavensward.
Emmanellain and Laniaitte also turn up in the start-of-Stormblood
Lv60 weaver quest in Ul'dah, apparently specifically to show off the High House costumes, so presumably trying to promote foreign trade.
And the lorebook profile for the Count de Durendaire is prettymuch all about his stance on foreigners - originally sharing Edmont's "desire to open Ishgard's borders and welcome foreign influences", but he became more conservative after the loss of his son. Now with the shifting situation in Ishgard he is supporting Aymeric "in a pragmatic bid to retain influence and preserve the status quo".