I usually handle that by changing the pad shape. For example you could make the press-fit connector pads ovals with the X and Y values exactly the same. Then In the options dialog for thermals you set ovals to flood-over. Of course, if you already have oval pads that you do not want flooded over - do it the other way around - Make the press fit the only part with round pads and make the others all ovals.
I've had good results from this method.
Good Idea. The only drawback is that these are library parts made by my engineer. I don't think he would take it well if I messed with his parts. I'm routing the ties manually, there are only four parts so it's not too bad.