I'm sure that it doesn't matter how you pronounce that last "ence" part...It's not like you're going around telling everyone, and it's not a test, so just say it how you think you should...I say it...With both "ence" and "ince"...I'm trying to see how I say it, but now I'm confusing myself
I probably pronounce the last part with an "ence" sound. I'm sure it's a regional thing, just like some people pronounce "aunt" so that it rhymes with "taunt" and other people pronounce it like "ant." Or CAR-mel versus "car-a-mel." (My dad and stepmother were horrified to hear me say car-mel once in a coffee shop, they said this was an uneducated white trash way to say it and that if I said that on a job interview it could cost me the job.)
When I first came across the word "incontinence" and had never heard it spoken before, for some reason I thought it was pronounced "incontinuance" and one day I said that out loud and my mom laughed at me.