Being personal may help.

When I get at work a message like:

"VP XXX is very interested in your feedback, it would be great if you spend 15 minutes and fill the form". I delete the email.

"Very interested in your feedback" and mass email do not work well. In addition I do not feel that my feedback given in this way will affect anything.

I do not think that it is your problem. You say that it is not a matter of trust, but I am 100% sure that it is.

I give honest feedback at 1-1 meetings.

By the way, did you read https://www.goodreads.com/book/show/52283963-the-mom-test

and

https://www.goodreads.com/book/show/1317946.Managing_Humans

? It could help :)