Cheating is a really bad problem, and very hard to resolve completely. I assume CodeChef is putting adequate efforts to detect plagiarism, but that doesn’t make people less likely to cheat.
I have a different proposal that is not going to eliminate cheating, but should probably reduce the impact that cheaters have: participation in long contests should be open only to accounts that have also participated, recently, in at least a couple of short contests too. If you have never taken part in CookOff or LunchTime, you should be not welcome to do Long challenges too.
What do you think? All contests remain ranked/rated, nothing changes here. Long ones just need some eligibility.
Please note that the parameters of the rule can be adjusted, and can be made very flexible and tolerant. For example, one participation in CookOff and/or LunchTime gives you allowance for the next two or three Long challenges (or even more, why not? say 6 long ones 
). So you have to take part in only one short contest to be eligible for many long ones.
This measure will:
- reduce the impact that cheaters have. If they have no real problem solving skills, one bad short contest will ruin their ranking and will demotivate them from doing their misbehaviour again;
- almost not impact the regular competitors, who are genuinely interested in problem solving. Scoring a high rank is good, but I think that CodeChef should encourage the perception that the rank is not a static achievement in time, something you earn and then quit to celebrate it but rather a dynamically moving assessment of your skills, relative to these of other competitors.
This measure is a form of commitment on that kind of perception.
For the extreme case of people who want to only do Long challenges, fine, they have their rights. For that specific audience CodeChef might consider building separate ranking system, scored from Longs only, and obviously allow everyone to take part in it, unconditionally.