Yes, you are entitled to reimbursment under article 8 AND compensation under article 7.

However I would assume that
A) this will invalidate any claim you have for reimbursement of the flight you actually took, and you'll be expected to use the monies you received to cover that.
B) KL will attempt to refuse you to pay the article 7 under the false pretense of "You chose to cancel the flight yourself", since this is a well known defense for airlines, and KL have a proven track record of being cheapskates with little regard for the law when they think they can get away with it.

An interesting alternative option would be for you to try and claim the cost of your alternative ticket from KL (and art 7 too if you arrived more than 4hrs later). Technically they were responsible for you to get from A to B so this is what they should do. You should probably have made that clearer when on your phonecall with them that you did find tickets and expect them to pay for it, and record the call to save as evidence in the future.

Maybe you can decide what to try based on the price you had to pay for that new flight.

It's weird that they rebooked you on another alliance for 24hrs later but didn't find you spots on the day when there clearly were some, that you found yourself. Perhaps you got them thanks to your UA status?