Right - firstly, spacing is NOT the same. 5mm for 7 speed and 4.8mm for 8 speed. So spacing is not the same and they are not strictly compatible.
BUT...
A lot of people say they are fully interchangeable and they presumably say that since they have done it and it works well enough.
Secondly, if it's only the largest sprocket it could be that the end stop screw (L) needs letting out a little. Although it could be that all the 0.2s in the spacing difference are showing themselves at the end of the sprocket...but just let the L end stop screw out a bit and see if that does it. But make sure that it's set correctly and doesn't allow the chain to drop between the cassette and spokes (bad idea).
Thirdly. Is the jumping caused by the chain trying to climb or drop onto the next gear cog? If it is, then it likely is the case that you won't get away with using the 8 speed mech. If not, then it's likely a stiff link in the chain. For that, check each link and if you find a stiff link, just use the easing plate on a good chain splitter to make it loose again. Then see if the jumping stops.