As KIB advised, but in a bit more detail.
So that includes the full exhaust hose and the exhaust mixing elbow that is often sold as part of the manifold in a marinising kit.
You don't say what type of boat this is, but seeing you give your location as Oxford and the boat name looks very like it is to meet the EA requirements re naming, it may well be a cruiser with a rubber exhaust hose, and if so such hose can and do delaminate at a point along their length and the delaminated section starts to burn through when the raw water fails. This causes a pocket that lets exhaust gasses (and water) past when at idle, but at higher speeds the gas flow pushes the "pocket" across the exhaust pipe, partially blocking it and allowing pressure to build up to such an extent it pushes back on the Jabsco impeller vanes and bends them back this stops it pumping. Seeing the cost of decent exhaust hose, I am far from sure you changed that. The delamination can be difficult to spot, even with the hose off the boat and pulled straight.
Likewise, I would not call the exhaust mixing elbow a pipe. These can and do gradually block with salt residue or in the case of the Thames lime scale. This also causes a build up of exhaust back pressure, pushing the impeller vanes back.
You have described pretty much the classic symptoms, unless you have (say) a bread wrapper caught on the raw water inlet so as you speed up the engine and water flow into the boat speeds up it gets sucked over the inlet, only to drop back when the engine stops.