Good afternoon, or whatever. I came up with this about eight years ago so I think it's about time I actually checked if it works.
There's only one spacial dimension (the one the object is moving in) to worry about in relativity and time is no different to space so you can derive time dilation and length contraction using two spacial dimensions. The four dimensions are at right angles to each other so if you draw a horizontal line and then draw another line the same length at an angle to it with 90 degrees representing the speed of light (so if you want to compare objects moving at half the speed of light relative to each other draw the second line at a 45 degrees to the first) then you just need to trace vertically down from the tip of the second line to see how much time dilation and length contraction there is by simply measuring how much shorter the second line is to the first one in the horizontal dimension.
You can see that at the speed of light the second line is infinitely time dilated and length contracted because it goes straight up. At low relative velocities there's very little time dilation and length contraction because if you trace down from the tip of the second line at low angles it's almost at the tip of the horizontal line but the same change in angle (relative velocity) makes more of a difference the higher the relative velocity. If you want to view the second line as the object at rest and the first one as moving then just turn it so that the second line is horizontal. In theory this should work perfectly. That's all of the relationships in special relativity expressed in detail and without a single equation. Actually all the equations are there but they're hidden behind geometry so simple it could be taught in primary schools.
If this does work then it should be able to handle acceleration as well be simply using a curved line. As the velocity increases, the angle changes to create an acceleration curve. As long as both lines are the same length it should work and the length of the curved line (it's length as measured by a straight line) should give you the amount of time dilation the accelerator experiences relative to the straight horizontal line of the inertial object, I think.