'Marginal performance' just about sums up most model stirling engines, power output is so low that everything must be just right for them to run at all. However if your engine is a tried and tested design from PM Research, or an original 1950's Davies Charlton
then it should be ok and run on a small spirit flame rather than a blow lamp!
The main enemies of success are friction and air leaks, clean off any old oil and relubricate with the smallest amount of the thinnest oil you can find. There is not much scope for dealing with air leaks if these are due to wear on the power cylinder or displacer rod, but ISTR there is a small blanking screw on this type which might be worth checking, as is joint where the displacer cylinder fits into the main body.
I don't know if the relative positions of the displacer on power cranks can be changed on this type, but they should be about 90 degrees apart (not too critical) with the displacer leading the power piston.