What do people do post-PPL?
For me, it just depends on the type of flight.
When I'm going to fly aerobatics in my usual spot (just outside the CTR), I just fill up the aircraft with fuel for 2.5 hours (for an intended flight time of an hour), start her up and head out. I don't create a plog, and I normally don't even open my map during the flight because I know that area from memory. It just sits there in my kneeboard "just in case". The only thing I write down on a scrap piece of paper, or the back of my hand, are the tacho and off blocks/on blocks times.
When I'm doing a relatively short x-country, with plenty of fuel on board, I typically create a minimal plog with a few waypoints, bearings and distances. That's either a separate plog, or a few numbers scribbled on the map. I don't do any wind correction or accurate heading/ETE calculation but just correct for wind as I go along. Unless I know that I'll be facing a howling headwind, in which case I don't go.
On long x-countries, particularly if there's a channel crossing involved, I typically go all the way, making a proper wind corrected plog with all the bells and whistles. That plog will also include my fuel planning, so that I can check whether the aircraft is using more or less fuel than expected. (Although the gauges in the aircraft are really not that accurate, so that fuel planning has to be taken with a pinch of salt, and a huge reserve in any case.)
the stopwatch in the aircraft seems to fail on an alarmingly regular basis
I have actually never used a stopwatch to time my legs. Just an analog or digital watch, or the clock of the aircraft, or the clock of the GPS. Whatever was convenient.
At the PPL level, the exam objectives are +/- 5 minutes, if I recall correctly. Any timepiece will do for that.