Simultaneous Turns + Activation

You could have pre-set initiative values for those activated abilities, where timing matters.

Something like:

1. Thunderstruck
2. Earthshaker
3. Summon Cthulhu
4. Everything else

And have a small reference card which lists the order.
Of-course this only works if you don't have too many of them.

Alternatively, if you were to have some sort of "characters" in your game, activation could be tied to the character.

Something like:

1. Gollum
2. Gandalf
3. Gimli

So Gandalf can use Thunderstruck on Gimli, to prevent him using the Earthshaker, but not on Gollum

I think that this is what you're saying about the speed icon, but just put a number on every card which determines the order any time there is a conflict. Mostly, cards don't interfere and people can just resolve their actions without consultation. In the cases like the one you've described, players know to look in the top right corner (or whereever) and see that Thunderstruck is #41 and Earthshaker is #26, so Earthshaker goes first, then Thunderstruck. Every number is different so there is never a question.

P.S. Don't number sequentially -- leave some gaps so that you can add expansions later with additional cards.

I have the same problem with a design and can spare a few ideas I'm comfortable with sharing.

Method 1: Each model has a preset initiative on activation with ties being resolved simultaneously. The models with the lowest initiative activate first to represent their ponderous nature because they may be a knight clad in heavy plate armor and wielding heavy two-handed weapons. Then you go in order from lowest to highest, resolving ties as you go. So if you have an initiative scale from 1 to 8 and you have two 4s you resolve them simultaneously before resolving the 5s and so on.

Method 2: During an activation phase of the game each model is assigned an action once activation starts and depending on the action the model does it may activate first before everyone else. To keep track of this, actions represented on cards or color-coded chits, whatever aesthetic is easier for you. With that said a model such as a rogue may activate first if they are assigned a move action to demonstrate their agility. This is indicated by modifiers on their card or stat line and they get an added bonus if allocated a specific action and the total score goes against the totals of other models. The object of this method is to have the highest number possible to force models to move first or to attack first or last, whatever situation calls for. Ties are resolved in the same fashion as method 1.

Method 3: This one involves D10 dice pools for each model with a preset number of actions and action modifiers. This has a little bit of resource and risk management since most models will have a dice pool of two (as in 2D10s) with some having more but it is up to you if you should use your best dice towards your first action or the last. It is your dice pool pitted against other dice pools. Just to avoid some power-gamey shenanigans you must have a card or chit to indicate what your first, second and optional third actions are in the order in which you allocate your dice to.

I hope these help you in your endeavor.