I wouldn't take a 555 to such huge time periods! Not that the 555 won't work, but you're depending on the capacitance and leakage of an electrolytic for accuracy.
To charge a 220uF from 1/3 Vdd to 2/3 Vdd over 2 min with Vdd=5V means the charging current averages around 3 uA, if I got the calc correct. But, pulling an electrolytic cap spec randomly off of digikey shows a leakage of 8.8 uA. Since the cap's leakage is unpredictable, varying by lot, voltage, age, and temperature, reliable operation seems quite dicey. The timing period could vary a lot, and it's possible that charging current could equal leakage and the time period is infinite.
For time periods like this, you can use a 555 with a more reasonable (shorter) time period going through a counter. But really, a PIC may seem to be complicated but realistically it's probably the best solution and is physically quite simple, although learning to use them has a considerable learning effort.