indirect speech - Modal verbs in reporting

'Advanced Grammar In Use' (AGU) by Martin Hewings, UNIT 37 C, says:

The verbs could, would, should, might, needn't, ought to, used to, and could have, should have, etc. don't change in the report:

'I could meet you at the airport.' --> He said that he could meet us at the airport.

'You should have contacted me earlier.' --> She said I should have contacted her earlier.

Is it possible, though, to have these pairs instead? (These are not from AGU but are made up by myself.)

'I could meet you at the airport.' --> He said that he could have met us at the airport.

'You should contact me.' --> She said I should have contacted her.

If these made-up pairs are possible, contrary to what 'Advanced Grammar In Use' claims, is it possible in general that the verbs could, would, should, might, etc. do change in the report?

If so, is 'Advanced Grammar In Use' wrong about this?