I've heard of taxes being paid in grain, but were barter economies the de facto system used by most of the lower class in the middle ages? Would it be possible for a lower-class individual to save what coinage they did come across to improve their station, perhaps across generations?
Im not an expert in coins, however, you forgot about the third option: non-coinage currency.
During the times you ask about, iron rods, blunt axeheads, blunt spearheads and arm-rings would often be used as a de facto currency.
This trend was so widespread, that to this day archaeologists find entire hoards of useless, blunt iron axeheads (which were never supposed to be sharpened into a tool, just serve as a currency) burried or stashed somewhere.
Up to the XIV century, iron and steel were of significant value, and thus it made sense to pay in iron.