You should not force players to make their moves under duress by giving them a ticking down countdown timer. A reasonable time limit might not be a bad idea to prevent AFK players from ruining everyone's game experience, but if you make the time limit too short, the game will become very stressful. You don't want players to lose a game because they simply didn't have the time to make all the decisions they had to. If you want the game to be stressful, you should build a real-time strategy game, not a turn-based one.
If you go the simultaneous turn route (which I would really recommend with so many players) then one thing you could try is only start the timer when a fraction of players already completed their turns.
But Instead of focusing on the timer, see what you can do to reduce the time it takes to make moves. In order to do that, minimize the number of inputs players need to make during their turn. The best way to do that is by checking which inputs represent decisions which are actually relevant. Try to remove any inputs which represent obvious or irrelevant decisions and focus on those which actually matter.
A good example for this is if you compare the gameplay of the classic X-COM: UFO Defense with its recent remake XCOM: Enemy Unknown. Some examples:
The first game had a "time unit" mechanic. Every soldier had a number of time units each turn. Every step a soldier took and every action they performed consumed time units. The player had very granular control over how exactly to spend each soldier's time units. So making a complete move with a single soldier could take 20 clicks or more.
The remake got rid of that by giving each soldier exactly two actions per turn, which could be used for either moving to any tile within range or for attacking.
The first game had different modes of attack for each weapon (aimed shot, snap shot, burst shot...). They differed by time unit cost and accuracy. Which one to use in which situation was kind of a math problem with only one optimal answer. The successor got rid of that.
The first game had a complex grid-based inventory system for each soldier which used a separate screen. To use an item which wasn't currently in one of the soldier's hands, the player had to go to the inventory screen, reorganize the inventory so the desired item was in the soldier's hand, and return to the actual game.
The second game also scrapped the complex inventory management. Every soldier carries one primary weapon, one handgun and 2 pieces of special equipment. All of these items are always accessible with a single click.
The first game had up to 26 soldiers in each battle, the successor only 6.
The overall design goal which the successor pursued with these changes was to reduce the number of clicks per turn as far as possible, but also make sure that every single click is a decision which has serious impact on the game. There are very few clicks which do not represent a relevant decision.
This makes the game not just fast-paced for the player, but also fast-paced for the spectating opponent. They need to watch closely what the opponent is doing, because each of their action matters for them, too. This also makes the opponent move interesting to look at in multiplayer games.
However, I am a bit skeptical if you will be able to pull that off with twenty players. Many actions will be only relevant for a few players, but not for all of them. I am afraid that with so many players, the only option is to allow everyone to make their turns simultaneously to avoid wasting too much of the other player's time.
You should also budget some development resources for tweaking the timing for the visualization of the execution phase. You have a hard challenge to overcome here. On the one hand you need to move all units quickly so players aren't forced to watch stuff which isn't very relevant to them. But on the other hand, you need to make sure that the events which do matter to each player get the screentime they deserve. Keep in mind that the visualization doesn't necessarily needs to be the same for all players. You might, for example, play a detailed animation for any attacks where their own units are involved and only do a very quick one for any where they aren't.
