Stubborn high nitrite levels are one of the most frustrating conditions in establishing a tank. You've fixed yours by cleaning everything out. At the bottom of this page is a column of "related threads." You'll see how other keepers approached this problem.
I don't recognize your readings (strips?). Usually we talk in fractional or ~5.0 ppm (parts per million). These are typical readings for the most-used API Freshwater test kit... a liquid test.
When you return and begin to cycle your tank, check out the "stickies" on cycling at the top of the menu in this section. Feel free to ask questions.
I agree with tekkguy that a fishless cycle is the quickest and most responsible method. But, do yourself a favor and use pure ammonia. (You'll thank me later.)