Mounting a 23kg 55" tv to stud wall on full motion mount?? UK
Your #2 idea to use some sheet material to span across the whole range of studs is the way to go. However do not use MDF or particle board. Both those materials have terrible screw retention problems. Instead use good quality plywood.

Also use thicker plywood if you can get it. 18mm thickness is a little on the thin side for this application. Try to get 20mm or more. The reason is that full motion TV mounts will put incredible stress on the mounting screws and you want to maximize the ability of the plywood to grip the screw threads and provide the maximal pull-out strength. 

Note that when mounting the plywood to the wall always use a pilot drill of the appropriate size for the screw threads into the stud. Sized properly the installed screw will be stronger than if you try to just brute force it into the stud without the pilot hole. The same thing for the mount screws into the plywood - use pilot holes there too. 

The size of the plywood sheet may want some consideration. If you can get substantial coverage over studs and still have it largely behind the TV than it will be easy to paint to same color as the wall and be hardly noticeable. On the other hand if it has to be larger than the TV then it may actually be aesthetically better looking to extend the plywood all across the width of the working surface.