Derek Hughes sells an overdrive upgrade as does this company
Sheffield Yorkshire providers of overdrive units
Or I have instructions for fitting a 5 speed Ford type 9 from a Sierra etc -- a popular upgrade with a lot of classics and I know one Bristol 400 owner that is delighted with the results.
I would have thought that Brian Marelli could advise at Bristol Cars
Come to think of it - this company look after more racing Bristol's than anyone else so would be best to advise
https://www.inracing.co.uk/ Ian Nuthall
The Ford option would be the cheapest..