Taking a look at the wiki on Clan War Leagues, there are two interesting points it makes (emphasis mine).
Aside from being in a league setting, Clans can still earn war loot and Clan XP in the same way as they do in a Clan War. Players can earn war loot that they've won even if they leave the Clan before the relevant war concludes.
Players can only be in one Clan's War League roster at any one time. Once they have been signed up by the leader for a particular Clan, their War League participation is only limited to that Clan. The player will only be eligible for War League rewards in the Clan he/she participates in.
Based on these, even though you have hopped around to other clans, since you can only ever participate for one clan in CWL during a given season, I would say you should still get your rewards, however note that I have never participated in a CWL so I cant say this is true from experience.