It's also enough to save and exit to the main menu and restart your open play. That's enough for me to get new missions. But personally it's too cheatish for me.Regarding missiin availability... it seems there a different bulletin boards in different game modes, so you might want to try a switch between open, solo and private group to find more missions.
I found some stations, where the station owner asks for scrap or nonlethal weapons, even though these are available at the same station the mission is shown. So you could exploit your rep with some factions, but it doesn't feel right.
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