Ok, how about this:
The Oster single burner hotplate ($20 at Target) has a cast iron burner surface. Instead of having a controller, or trying to manually follow a profile, you buy two hot plates, set the temperature of one to 180C and the other to 220C (confirmed as stable temps by cheap-ass thermocouple meter).
After both are fully warmed up, put the board on the "soak" hot plate until it reaches soak temperature (confirmed by thermocouple) and for an additional two minutes, then move it to the "reflow" hot plate until it reflows. Then move it back to the soak hot plate for just a little while, then to a room temperature surface until it cools down.
Kinda like the fancy ovens with multiple zones.
Of course this depends on the Oster being able to maintain a temperature reasonably well.
Fundamentally, instead of trying to change the temperature in accordance with the profile, with controllers, solid state relays, ects., you fix the hot plate temps to the two critical temps in the profile - the soak temperature and the reflow temperature - and then measure the temperature of the board as it reaches soak temperature and set your timer for the appropriate soak time. The reflow part is pretty simple, based on observation. And then whatever works for cooling.
With a little experimentation, you might be able to convert all this to a simple time protocol - so much time on the soak hot plate, then so much time on the reflow hotplate, etc.
Anyone ever try doing it this way? Total cost would be under $50. No assembly required.