I am managing a refurb job. The client really wants the sink in an island where no waste pipe is. The joists run the wrong way to run anything between them. My first and most ideal option is to run the waste above the joists and build floor up around it, I have 70mm allowance. The run to main waste is approx 4m, I wouldn't be able to add much of a a slope though in this length. I also don't want to cut into joists as this is not ideal. Do you think this could work? The other option is to put a pump under sink but I have no experience with this, i.e. noise> Can anyone recommend the best available in terms of noise and any suggestions.

Tell the client it is not possible, this work is subject to Building Regulation 'H' and I think you would have igning it offtrouble complying with them and have an Inspector signing it off.
There are strict regulations governing pipe size and fall.
The biggest concern I would have is plumbing a dishwasher into a waste pipe of that length without the expectation of constant blockages occuring.
Easy access would have to be available for High Pressure Water Jetting as this is the best way of cleaning out soap and fat build up. Even worse if a waste disposal unit is fitted.

32mm max length of pipe 1.7m
40mm max length 3m min 18mm/m fall

We use glue up pipe size LA traps instead of tubular as well, they are more ridgid long lasting. The 2" is a good idea if it is already there but, I wouldn't rerough just to up size. Plummer