The compact crankset is a good idea. It will not require any other parts except possibly a different bottom bracket cartridge, and for work, just a shortening of the chain and slight dropping of the front derailler. It will help quite a bit.

The problem with a bigger cassette is that your rear derailler may not be able to handle it. My guess from the original gearing is that it is a short cage derailler and the hanger on the dropout is short, too. Once you have to change the rear derailler, things can cascade expensively from there.

More radically, a 46/30 chainset should sort you for at least a decade. The cheap way to do that is to find a decent used 110/74mm BCD triple chainset and run middle and inner rings only. Again, no other changes except a shorter chain and repositioning of the front derailler. Specialties TA (Peter White Cycles in US, Spa Cycles in UK) makes every chainring you could ever want for 110/74 cranks. Or, look at the offerings of Rivendell Bikes if you want a tidy solution.

oldschoolbike