For what my 6 eggs are worth........
I'm a lazy sod, I learned years back, from a particularly evil sergeant called Robinson, do it once, do it right, so, taking the best of points from the previous posts
Work out where you want the CS to end up permanently, then knock up a concrete base, a cube or yard in your case!, ain't too hard and is cheap enough if you can get the gear in in bulk with a trailer, so you only have to move it once.
Put the conduit for the cables, exhuast fuel supply, as required in the base before you pour it.
Cover the cs with what ever it's under now
Whilst sorting out the new shed save, scrounge, steal the makings for an engine shed and build it around the CS as time and finance allow.
Easy on paper, ain't it!!
Cheers Stef