So I play a large number of various board games (mostly eurogames), just wanted to share a few mechanics that I think might map well to a competitive setting (idea dump):
Hidden, but global objectives. One example of this would be the game Santa Cruz. The idea here is each player has two objective cards that can be played to give points, but when played, they give points to everyone. An example: one gives 3 points to each player for every river adjacent location they control. So you never know exactly if someone has this card (as river's can be quite nice for expanding over a distance), but if you are too obvious about only grabbing river tiles, then everyone will suspect you have this card. Another fun aspect here is that it costs a turn to play one, so it might be worth it if you meet a condition and one of your opponents is close, but it also sets you back towards meeting the conditions your opponents might have.
Common global objectives that have a higher reward if less people have achieved them already (I.e. in Thrun and Taxis, the first player to finish each goal gets one more point than the 2nd person, who gets one more point than the third, etc). Even if you and another player achieve the same goals over the course of a game, the order you try to achieve them in can make a huge difference.
Some sort of limited resource to compete over. See any worker placement game ever (such I.E Agricola,Stone Age, etc), most of the 4x simulators (Eclipse, Twilight Imperium) and many others (Saint Petersberg, Dominion/Thunderstone/Ascension, Vikings, Power Gridetc). I suspect that this will already be in there in some fashion as all players are interacting with the existing locations and units for each of the two factions, but might be worth pushing for more of this, as it generally leads to more interaction between the players. Such as in Eclipse, you might sacrifice an early turn to grab a crucial tech, and because of this lose out on being able to explore and control the direction of the wormholes in a crucial area. Many of the boardgames that my group hasn't enjoyed lack much interaction, and it basically a bunch of people playing solitare against the same random draws. One idea here that might not work well with simultaneous turns is having some global limit on the number of each type of action that the pool of players can take (scaling with number of players of course). Not exactly sure the best way to work this into a simultaneous turn without rewarding someone who clicks/plays faster. Another example would be power grid (bidding over the power plants and limited fuel supplies). Could perhaps start each round with some sort of auction for access to something to add this in without going fully turnbased.
A food clock(or whatever you want to call it). A prime example of this Agricola, where you need to feed your family every so often (with this ramping up later in the game so you have to balance development with short term goals). You already seem to be hitting this with the edict idea. This doesn't necessarily have to be a game loss, but could easily instead be significant point loss or some other sort of opportunity loss (don't gain access to some extra action if you fail this "quest") if you don't meet the criteria (see also games like Trajan). (I.E, control 4 cities by turn 40, for each city you are missing, -10 points). Having strict loss conditions can be poor if its intended for group play, now one of your 4 players is out of the game (rather than just behind and still possibly able to influence the outcome or even come back). Kingsberg does this by having invasions (with some randomization), that you have to deal with every so many turns, etc. - This would prob be good even for a single player setting, as its nice to force people to balance longterm + shorterm.
Some randomization besides just mapgen, but not too much. (Example: Through the ages -- Even though all "random" events besides the first few are chosen by the players, when they happen is somewhat random, and what order the various techs become avail is somewhat random as well). Just wanted to make sure that it doesn't boil down to, evaluate starting situation and calculate the optimal flow of the game from there, but also that there isn't too much. Our group no longer plays Settlers because the game is a bit too random, nothing like a game where 6 of the first 10 rolls are 11s. Seasons is a much better example of adding in randomness in my opinion, where the first player (which rotates in each round), gets first choice out of a number of dice showing various choices, but then the 2nd player gets to pick out of what remains, etc.
Barter of some sort? Unsure if this would fit here, examples might be 7 wonders, where gaining access to resources lets your neighbors buy them (which gives you money to then buy other things or resources from them back), or less likely, an actual barter system like settlers of Catan.
Other player interaction could be like Puerto Rico or TI, where each action you take gives some (lesser) benefit to the other players, again might be hard to adapt to a simultaneous move game though?
