The problem is that the controls point to a resource file (I'm assuming) in _content
The Radzen Blazor components do not include a resource file by themselves. The developer does that (step 3 from the getting started instructions). Or if using Radzen - it generates it in the _Host.cshtml file. You can simply replace that reference with your copy of the stylesheet.
The icons are all simply text.
Yes. Radzen uses an icon font (Material icons).
How can I completely overwrite the styles with a secondary stylesheet?
Your best bet is to copy some of the built-in themes and update it as you need. Radzen itself includes a theme builder which allows one to visually customize a theme (still not replace all icons).