I'm trying to bind (clojure.tools.namespace.repl/refresh) to a keyboard shortcut. I managed with cider-interactive-eval, but the problem is that the "minibuffer" or whatever it's called that comes up isn't big enough to display the complete output if there was an error. Can I make the output go to the repl instead?

Some output goes to the repl, but a stacktrace comes up in the minibuffer and it's not big enough.

in cider-interaction.el there's a function cider-refresh that should do what you want

and it's got its own refresh-response-hanlder to do exactly what you want

and you can hook up pre and post functions to run, and some other options

"Reload modified and unloaded namespaces on the classpath.

With a single prefix argument, or if MODE is `refresh-all', reload all
namespaces on the classpath unconditionally.

With a double prefix argument, or if MODE is `clear', clear the state of
the namespace tracker before reloading.  This is useful for recovering from
some classes of error (for example, those caused by circular dependencies)
that a normal reload would not otherwise recover from.  The trade-off of
clearing is that stale code from any deleted files may not be completely
unloaded.

With a negative prefix argument, or if MODE is `inhibit-fns', prevent any
refresh functions (defined in `cider-refresh-before-fn' and
`cider-refresh-after-fn') from being invoked."