Some stats like ours are just held (though a cut-out in the tank insulation)
against the wall of the tank by a stainless steel belt all the way around
the tank, and tightend with a screw adjuster. i.e. they are not actually
bolted TO the tank.
If this was the case, it's possible (assuming the c/h fitter left enough
cable slack on the stat) the belt could be removed - or cut off and
replaced if you can't get to the tensioning screw either directly or by
moving the belt around to where you can get to it. Stat would drop off and
could be fished out and replaced. Another cut out could then be made in the
tank insulation to fit the new one where its more accessible. An hours job -
even if the cable to the stat needed to be jointed/extended a bit.
It probably would take a good few hours to move the tank around if it HAD to
be done, but if it was me, I'd be getting a mirror and a torch and having a
good look behind myself first.