While I'm thinking about it, a clarification...
Mission board refresh 'spam' button: Bad idea
Mission filters that refresh the board: Also bad idea.
The increased server load could be immense. Don't do it.
No, the way I'd do it, as already mentioned several times would be to generate a stack of missions with a priority variable. If the display is only capable of presenting say, 60 missions at any given time to the player, push the highest priority missions to the top to simulate how busy the station is and the competitive spirit of the NPC's trying to get their contracts filled and show LESS of them so they're ALL at least partially relevant to the current ship to improve engagement and choice, while still enough to offer a full selection of reward options so the player can choose what they actually want to do, and get out of their play time. I'd also consider REDUCING the current mission stack, down from 20 across all mission classes. You may not be able to stop players trying to fill their stack, but you can make it twice as easy to fill, by halving the size of the hole.
So, you can scroll through 60 missions, pre-filtered based on the ship you're in but in the background there could be literally thousands of available jobs, either client or server side, or some low overhead combination thereof. If you narrow the selection by changing the filters you should still be seeing the highest priority contracts, because those are still the ones the NPC's are competing with each other to have filled. Changing the filters should not allow the player to regenerate the board ad-infinitum and overload the mission server. All the filters do is bring missions that 'fit' what the player wants to do or achieve, and preferably both, from the priority stack, into the visible list, in priority order.
When you ACCEPT one, then the board is refreshed, with newly available missions being added to the existing priority stack. Using the same server transaction that logs the acceptance is going to reduce traffic and give a more real-time interaction. The parameters of the ACCEPTED mission(s) should be used to refine the filters and automatically present similar missions to the player so they can fill their hold more quickly and efficiently and carry on with their game instead of being forced to sit there, bored. Developers no longer have the luxury of limited competition, or extra-goldfish attention spans. There are plenty of other games that don't make you twiddle your thumbs for 15 minutes and people will simply tune out, and play something else. Or worse, actively come up with ways to get around what they now perceive to be a problem worth circumventing. Games don't take 30 minutes to load from an audio tape any more, even though some of us remember when they did.
Yes, it may be a little confusing for some players to begin with, but ED is notorious for it's steep learning curve anyway and many players have already accepted that it's worth keeping an eye on a certain handful of youtubers for tips and hints, even if there is an official tutorial video from FDev which, if they were accessible in-game would be a big improvement for on ramping new players. And, if the videos could be converted into actual gameplay tutorials, even better.
The bottom line is this: Gamers are not stupid, they have agency, and will use it to 'game' any system with a reward on the other side of it. Some of them have been doing it their entire lives, so they're very good at it. Accepting this and instead, offering them what they want so they stop breaking your s*it to get it anyway must be a smarter move instead of chasing them around trying to put the fires out. They significantly outnumber you FDev. They also have access to military grade, instant communication systems and will band together to make your life difficult if you upset them, and often when you don't. Who'd have kids, eh?
Reality check: They will not stop! How many times does this need to be made blindingly apparent before some notice is taken and another mitigation tactic considered? Don't give them everything 'instant win' style, but there must be a happier medium where they don't feel like their time is being wasted, and you still get hours and hours of engagement.
[Edit: Something else I'd seriously consider, despite it being wildly unpopular, at first, is to significantly REDUCE the individual payouts on any given mission, such that they don't overwhelm the trade economy. If you make it MUCH easier and quicker to fill a stack of half as many missions while reducing the payout on all of them, such that the player still ends up with a net gain of 10% more profit per hour invested due to less 'wasted' time trying to build an efficient stack of missions, then you might be onto a winning formula.
If reloading the game becomes more of a time sink than simply accepting a mission you want and instantly having another relevant, yet slightly less attractive option popping up from behind it, it's easier to take that one too and see what's next than board flip. If the RNG is also adding new missions every three or four times you accept one, pushing the reward back up to optimal you might find players are more willing to 'try their luck' on getting the gems and get less upset about it being near impossible to find a set of them that logically go together to make a coherent and efficient "run".]