Halliday & Matthiessen (2014: 522, 522n):
On the other hand, many verbs that assign interpersonal and/or behavioural features to the speech event, and are used to quote especially in narrative contexts, are never used to report because they do not contain the feature ‘say’. Thus we are unlikely to find … Poirot mused that discretion was a great thing, and even more unlikely to find examples involving behavioural processes that are closer to the physiological end of the behavioural end of the spectrum.*
*But they do occur when they embody assessment, as is illustrated by the following selection from the web:(a) Drinking in the view across the Potomac River, Kennedy reportedly mused that he could stay in that spot forever;
(b) When we invented the wheel, people moaned that we’d forget how to walk;
(c) Citizens have long grimaced that their votes are the only input they gave into government;
(d) I muttered, embarrassed, something about having never been to see him all this time and she frowned that I had never gone to see him;
(e) The careful telephonic questions of Dictator Mussolini were followed by abrupt commands. Consul Riccardi gulped that he understood, hung up, donned resplendent attire, and fairly strutted to the residence of Provincial Governor Stumpf.
However, there do not (at the time of writing!) appear to be examples of reporting with hiccupped (hiccoughed) that, coughed that, spat that.