If you don't believe in time dilation, then why are you trying to explain it with just length contraction?
How can a clock have the same rate yet specify a different time? Don't you understand that an observer traveling with the clock will use the flashes of light bouncing off a mirror as a basis for time? If he has two clocks at right angles to each other and the light bounces at a different rate for one of them than for the other one, then he's going to have a device that will detect absolute motion. Is that what you are promoting? And it doesn't matter if it is a light clock--any clock will behave the same way.
If light only has to travel a shorter distance, wouldn't that mean the clock was ticking more rapidly?
I didn't say either one of those things--Einstein did. And you should read what he wrote and try to understand it and believe it instead of trying to work these things out on your own.
Why don't you start with his 1905 paper introducing Special Relativity
? In section 1, you will see where he talked about defining
distance with a rigid ruler:
Following that, he goes on to talk about the definition
of time, both local and remote.
I really don't want to discuss your personal ideas about these things but I would be happy to help you understand what Einstein said about them. Do you want to give up on trying to explain these things better than Einstein did and learn what he had to say?