Nitrates are the end product of the cycle, so having high nitrate numbers means your cycle is working fine. A heavily planted tank would help with the nitrate levels, but not enough to keep up with 160+ ppm! I read somewhere a while back that if the water parameters get too out of whack the bacteria slow down their conversion rate. I think your 2.0ppm of ammonia is due to the excessive levels of nitrates in the tank.
As for rinsing filters, whenever you do a partial water change, fill a 5G bucket with the old water and rinse all your filters in that. This will prevent killing of the bacteria. Also, rinse only enough to clean, don't get crazy and scrub all the bacteria out too.
Do a couple 1/2 WCs two days apart and keep testing the nA levels.
Also, as you just came off a algae kill (the blackout), that is why the levels spiked. The dead algea remains break down and will increase the A, nI, & finally nA levels as they decay. It's the same as having a few dead fish rotting away.