I request your assistance one more time. I am in dire need of help and I'm frustrated as can be. You see, I have to teach (ESL) the use of several time sentence connectors amid which there's by the time.

I understand how to use it and more often than not I am able to tell when it is being naturally used and when it is not.

The problem is that my group is in a beginning level and I can only work with simple past and past continuous.

Certainly, you can use by the time with both as in:

By the time I arrived, my parents were eating dinner.

I see that it feels awkward when you try to join two simple-past clauses. For example:

I cooked dinner by the time you went to the shop.

I guess it's not entirely wrong, but it feels strained somehow.

So here is when I start getting frustrated. I say, OK, you cannot use by the time to join two simple-past clauses together. The problem is, sometimes you can!

I finished cooking dinner by the time you went to the shop.

I was tired by the time I finished.

Why is it different now? What changed? Why can we sometimes use by the time with simple past only and why can we not on other times?

I hope someone can walk me through this. I'd appreciate it a lot!