When this bike was referred to as a ten speed... that was 5x2 to get ten.
the frame spacing was 120 mm
your wheel set is probably 130mm
the frame will need to be spread apart.
not sure what those Miche hubs were set up for. Appears Shimano in spline form but you need to reference from where purchased the cassette width ( by inference the number of cogs it can take )
700c is 4mm smaller in radius than a 27" rim...
pretty sure there is room up front to drop the pads, not sure at the rear.
if a 8, 9, 10, 11 cog cassette is required you will probably need a newer rear derailleur with more "swing" to catch the largest rear cogs.
the current front chainrings won't accept a 9 or 10 cassette- too wide. Needed chain too narrow.
this is not a plug and play project.
I would save the wheels for the next bike, use the wheels that came with, new brake pads, cables. Not sure what to advise on the derailleurs- do not know what you have.
setting aside Simplex is a rational thing to do, you might be married to those levers. As I recall one side of the shift was brazed on, the other side on a clamp, unique to Simplex.
the problem with those levers is they do not pull a lot of cable in total.