Specifically for E53 (rather than E70) –

I don’t think that the ZF ‘box (6HP26) was ever fitted to the 3.0 litre petrol (gas) models, only to the 3.0 litre diesels from 2003 onwards

The early 4.4i & 4.6iS petrol (gas) models used the 5-speed ZF 5HP24 transmission and then the 6-speed ZF 6HP26 unit took over for the 4.8iS

The GM 5L40-E unit certainly had a bad reputation with the 3.0 litre diesel engine but maybe it was a better partner with the petrol (gas) engine in terms of reliability?

Phil