Well, I wouldn't say there is a mapping per se, because the problem style is different (on Codeforces it's mostly about thinking, in Codejam — thinking plus coding). Even Codeforces GMs, for example, sometimes solve Round 1A in 8-10 minutes, while sometimes a div. 2 F problem receives its first AC just after the beginning of the contest. So it's not very easy to compare the two. The qualification round is especially tough to map since it lasts 27 hours (CF rounds last only 2-3 hours).

That said, I would say that the first several problems of the qualification round (i.e. the ones needed to advance) could be rated 1300 or even less. I had almost no problems with passing even when I just entered CP. This year's problem D is ~2000, problem E maybe ~2500. (I'm talking about the Larges, the Smalls are well below 1900). But again, you get 27 hours to solve them, so it was rather realistic even for a purple to solve the entire set (I got everything except E-large).

Round 1 is something like 1700 — 1900 — [2000, 2500], and that heavily depends on the problem (again, the larges). But to advance 1700-1800 is enough (I passed for the first time when I was mid-cyan).

Round 2 has a bit more variation, this year I would have given it something like 1800 — 2000 — 2300 — 3300. I guess ~2100 was enough to advance (but I know CM's who did and GM's who didn't...)

I haven't analyzed Round 3 and WF very closely, but I think Round 3 lies completely in the [2100...] range, except for maybe half of the smalls and the easiest large. Advancement is strictly on the GM level (however, there have been LGM's who failed to advance and AFAIK several masters who managed).

I think the above mapping is valid with a delta of +-100, because it's hard to estimate the difficulty objectively. But yeah, something like this sounds good.

Also, I wonder why you haven't posted that from your main account? :)