It doesn't seem right at all that the stove back boiler is not connected to the cylinder. If the cylinder is too far away then a buffer tank somewhere over the boiler should be used both for safety and to allow stove to reach operating temperature. The pump would be used to distribute the heat from the buffer tank instead of from the stove. The Dunsley would allow gravity circulation but would not have enough capacity to absorb overheating if the power goes off. It is dangerous to have header tanks overheating, they can melt and spill scalding water into rooms.
when I reread the OP I notice that the cylinder is on the ground floor... Which indicates that both the oil and Stove are going to be pumped systems. I don't think a Neutralisers is going to be suitable for the OP as they are not too great when being operated with a pumped system, its too easy for the water to be just circulated through the neutraliser.
Sounds like the Flow and return from the Herald are just tee'd into the upstairs heating circuit, with a pump to boost circulation.
I'd reiterate again that the location of the pump on the stove pipework is the most likely cause of the problems irrespective of how much the installation conforms to part J.
Tiggers layout is a fairly typical use of a neutraliser as both the heat sources are gravity cycling to the neutraliser and from the neutraliser to the cylinder with a pumped take off for CH.
When you study the Dunsley diagrams the neutraliser is always located near or just under the cylinder. THe 'c' type being a case example as its designed for the cylinder to sit on top of it. IF academan's cylinder is on the ground floor then a neutraliser would be about as much use a a chocolate teapot.
The OFTEC reccomended method of dealing with multiple heat sources such as oil/WBS is to have two totally seperate heating systems, which is just plain silly TBH.
I think with a few modifications to the existing pipework it would be perfectly feasible to allow the stove to supply both CH and DHW demand, however this may not be desirable dependent upon the size of the property.
Whatever you do, action is imperitive becasue if like your current plumber states you are getting pumpover to the header tank then you will be introducing lots of Oxygen to the system which will dramatically increase corrosion and lead to premature failure of either of the two boilers, as well as increased levels of corrosion in the radiators. If the heating is microbore you will have a fair chance of blockages due to sludge, and the effective lifecycle of any inhibitor added to the system will be greatly shortened too. I don't want to sound all doom and gloom, this could probably be fixed very easily.