The adjective simultaneous—and the related adverb simultaneously—are ripe for a new English word. Not only are they overlong and over–Latin, but they mean something which is fairly basic and should have an easier word. It is easy to swap them with the phrase at the same time, but it would be better if we could have something shorter and ‘snappier’.
I would thus like to put forward the new word sametime to go in its stead. This word takes the phrase and shortens it into one word. So, “Thomas Jefferson and John Adams had almost simultaneous deaths,” becomes, “Thomas Jefferson and John Adams had almost sametime deaths.” Which I think works rather well. For the adverb the new word would be sametimes. So, for example, Shroedinger’s car is “simultaneously alive and dead,” or, “sametimes alive and dead.”
The word is shaped on sometime and sometimes, which overset occasional and occasionally. This likeness to an already existing word makes it more likely that it will be understood without worry or hardship.
Roots English 
Hi there, I actually use “sametime” myself; it’s one of my “phrase words” (words from phrases, as opposed to phrasal verbs).
I like it a lot when the same answer comes to each of us, but without having spoken about it. It shows that it is more likely to be inbuilt–or at least fairly logical–to English as it is today.