Walk in the park for a man of your intellect and skills. Search out those Whitworth Spanners, "read the books "....find BSA Service Sheets in the Forum Literature Section and away you go.
With barrel etc already off, the whole engine and gearbox unit comes out as a lump. Split off the primary drive, timing covers, dynamo, gearbox and the cases can be split. You may need a claw extractor for the crank timing pinion, but otherwise it is straightforward and all detailed in the books.
These engines do suffer from accumulation of sludge and debris in the crankshaft cross oilway, the so called sludge trap, and a strip and clean on any unknown or neglected engine is well worth doing to prevent future expensive inconvenient failure. Bear in mind big end bearings always have a little sideways rock, but should have no up and down movement. Crank endfloat is supposedly a mere 2-5 thou if you're lucky. Most have a fair degree of slop and run quite happily. YouTube is a good practical source, well worth a look.
Plenty of horror stories about so called professional builders. Have a word with Bergs about one of his recent back from the dead renovations....an extremely well deserved success against a background of some of the most ill thought out engineering codges by a so called expert we have ever experienced.
Don't condemn the pistons without close examination, the rings are the most likely failure. A distinct wear ridge at the top of the bore is a further indicator. Good used pistons have a value to those rebuilding on a budget, don't simply discard them.
Swarfy.