1. I will do it when you help me

2. I'm going to do it when you help me

3. I drive when she sleeps

Let's say I want to report these sentences. If they are still true or yet to happen I leave them unchanged for instance "He said Greg will do it when she helps him". On the other hand when those statements are no longer true we report them for instance "He said Greg was going to do it when she helped him". This part is completely clear to me. What bothers me is that I saw one more variation "He said Greg would do it when she helps him". If it is correct, can I do the same with other 2 sentences and write "He said Greg was going to do it when she helps him/He said Greg drove when she sleeps. Explain why yes or no and the difference between them. Thank you.

Ps. There is no intended meaning. I once saw that this sentence "I will do it when she arrives" was reported like this "He said he would do it when ahe arrives". I don't understand why only part of the sentence was back shifted. If it is correct can I do the same with other sentences I mean that I back shift only one part of a sentence?