Randomise post order within custom category view

I have a custom category created with custom type posts assigned to that category.

Everything works fine, when you view the category, we get the list of custom posts in DATE ORDER.

What I need is a hack that will always display this listing of custom posts in RANDOM order. I think this can be done without a plugin?

I’ve tried everything, e.g. creating a new query object and setting orderby to rand. Unfortunately I just can’t get it working so that it displays the posts in a completely random order.

I’m thinking that I need to delve deeper and back to the original SQL query.

Any guidance on this would be much appreciated.