So, you draw up a space-time diagram, with 3 dimensions of space and one of time. The time dimension is really easy - you simply graduate it in your minutes, and also mark off each of my seconds (at your minute marks). Two events then happen - were they simultaneous? Simply check the time scale.
The trouble is, as you noted above, that everything must be reciprocal. If you see my clock ticking 60 times slow, then I see yours ticking 60-times slow relative to mine (ie. my clock advances a minute in the time it takes me to see yours advance a second). Remember, my view is every bit as "valid" or "real" as yours. Equally, I can also draw up my space-time diagram, graduated with my units.
So, lets combine yours and mine space-time diagrams into a "God's-Eye" view. How would we draw up the axis for the time dimension such that it accurately captures the fact that one of my seconds equates to one of your minutes, together with one of your seconds equates to one of my minutes?
Clearly, this is impossible - which means the concept of a global time axis is also impossible. This, in turn, means it is impossible to give a unique global (ie. over all frames) time coordinate to an event. This renders the attempt to state that two events have the same "time" coordinate across all frames as futile.