For forced flushing, regardless of the liquid used, get a 60 ml luer lock syringe from Tractor Supply ($2.99). Then take a carto condom, cut off the closed end, slip it on the carto and syringe, and you have a cheapo carto cleaning device.
You can also use the same device to fill your cartos. While you are at TS, pick up some long 18 g needles. They are perfect for reaming out the center of a carto that is beginning to draw hard. You stand a chance of wrecking the carto, but if you are gentle and rotate the needle slowly, you might be able to save a few cartos that have stopped performing. The reaming technique only works with the vertical, single coil cartos.
I use Liquinator tanks which are real juice hogs, but they keep the carto moist without flooding. The three I purchased are over a year old, and they still work well.
These are not my ideas, but they were posted in ECF a while ago. There are a lot of helpful hints here, but at times, it is a bit of a bear trying to dig out information.