My first message is that if you get a chance to contest the "ruling" that you argue only for yourself and that you leave others who are being treated similarly to argue for themselves. If you didn't cheat, just be clear and consistent that you did not cheat and that some other phenomena, unknown to you, must be responsible. Full. Stop.
Issues about multiple choice tests
Good multiple choice tests are hard to design and not everyone does it well. People make mistakes in phrasing and the phrasing can confuse test takers.
Presumably the students all had the same instructor. If there was anything in the instruction process that left the students in some ambiguous state, perhaps subtly misunderstanding some point, then many of the students will have precisely the same misunderstandings. In a course delivered over the internet, with lessened student-teacher interaction this can be expected to be higher than normal. If any question on a resulting exam touches on that topic, then many students will be led to answer incorrectly, but similarly.
So, a group of students turning in identical multiple choice exams is not, of itself, evidence of misconduct. First you have to weed out all of the correct answers. Next you have to account for similar misconceptions and misreading questions with poor phrasing, etc. Only the remaining ones have any validity at all, and, even when a test is well designed, students may be subtly led to the same answers. And your suggestion that you answered about 3/4 of them correctly reduces the set on which any conclusions might be drawn.
Students are often taught to go through all the questions on an exam and answer only the easy ones (or none at all) on the first reading. If students actually do this, and the easy questions are distributed through the exam, it would be natural for students to answer questions independently in roughly the same order as their peers, again, since they had the same instruction.
I don't know of any actual research on this phenomenon, but, importantly, I doubt that there is research that refutes it by suggesting that students generally answer questions in precise presentation order or random order. Low hanging fruit first. Then make a second pass.
But to say that a group of students answered the questions in the same order is, itself, evidence, much less proof, of misconduct, is a stretch.
I think it is a serious error to try to take processes, however good (and I doubt that multiple choice tests are in that category), that work in face to face instruction with proctored exams and simply try to move them to a completely different environment for which there is little research and little instructor experience. To layer on that an assumption that some intervening "sophisticated" technical system will simply "work" and also reliably tell you things that you couldn't know in a standard environment, is, in my view, preposterous.
I would, as a CS professional, want to know how the technical system was tested and verified and whether there is any provable validity at all to making the assumptions described by the OP.
Issues about timing and internet servers
There is some question about whether the OP really means "identical timing" or merely "very similar timing". I don't think that even a bot trying to achieve such a result could be successful due to internet latency. The internet is fast, but it isn't instantaneous. A very coarse clock, one with a tick-time of several seconds, might show patterns, but they would be imprecise at best. I'll assume that the students were not all on the same local network and were distributed. Certainly a bot spoofing a set of students from a single location could achieve very close, but not identical, times. To spoof several, it would need to fire several transactions and each would have its own latency. Some of the requests might actually interfere with others.
But if you add in human latency the problem of achieving near simultaneity becomes impossible. Suppose some individual - the best in class - is solving the problems and providing answers to everyone else. They send out an answer, but very most likely, would do so after entering their own. What would induce them to wait? Why would they try (or even think about trying) to achieve simultaneity of answers. The answer is received by the cohort. The incoming message has to first be recognized by the individuals (latency), they have to find the question, possibly by scrolling (latency). They have to enter the answer at human speed (latency) and then submit it. Then, assuming that they are not co-located on the same network, individual net requests go out (latency) and picked up by the server (fast, but not simultaneous - I doubt the server runs on a Cray parallel machine). Servers cache things, which can confuse arrival times which must be entered (sequentially - again, fast but not simultaneous).
Caveat: One can remove most of the human latency issue by using something like Zoom or a Skype conference in which everyone is able to watch one of the cohort in near real time. If all members stay synched on the exam page then when one makes a move, the others can all answer quickly after the first. If the "lockdown browser" is effective then Zoom would seem to require a costly setup for the cohort.
If my assumption about not being co-located and not being a bot in operation are correct, I conclude that the timing values are spurious data and you should look to the operation of the software (the server) to account for it. As Harry Potter might say: Riddikulus.
Something is wrong. The exam structure itself is (IMO) flawed. The imputed "data" about timing is deeply flawed. I doubt that it is reproducible. Drawing conclusions of misconduct from it would be wrong.
This is why I have, in several posts here, suggested that we need to rethink student evaluation, among other things, in this new environment. And the caveat stated above, if Zoom or Skype could be used in that way suggests an even more important reason to update methodology from first principles.
But, the bottom line here, is that if you did no wrong, just insist that it is so. Illegitimi non carborundum.