Those sentences seem fine to me. Probably the use of the simple past would be more usual in American English than British English.
The tense in reported speech doesn't always change. Thus:
1. In a report of a very recent conversation, you can use an original present or present perfect tense, e.g. "MissQ says she has broken her leg". (Original: "I've broken my leg!")
2. When reporting something that is still the case, you can use a present tense, e.g. "My teacher says the earth goes round the sun!".
3. When reporting a statement in the simple past tense, you can use the past perfect or the simple past, e.g. "He left a year ago" => "I said he left a year ago" or "I said he'd left a year ago".