The gemara says that Elisheva the wife of Aharon had a husband who was kohein gadol and a brother in law who had the status of a king. The gemara questions whether Moshe had status of a Kohein Gadol also, and ends up with a machlokes tana'im, but all agree that he had the status of a king. Even Ulah who says that Moshe wanted to be king but was never granted rights to be king, concludes that he himself was king but it wasn't bequeathed to his children. The idea that Moshe had status of a king is also confirmed by the gemara in Shavuos that15a that to give kedusha to the mishkan there had to be a king and a navi - rashi explains that moshe had status of both a king and a navi. Rashi in Bamidbar (10:2) on the pasuk of making trumpets says that they should blow before Moshe "like a king, as it says ויהי בישרון מלך" (although Rashi in Devorim (33:5) doesn't explain that the pasuk refers to Moshe).
Rav Moshe Feinstein (Dibros Moshe, Kiddushin Hearos on daf 37, heara 57 - pg. 542) raises a question. Although the pasuk refers to Moshe as a king, he didn't seem to act as a king. A king cannot forgo on his honor, yet we find that Moshe was willing to go to Dasan and Aviram and forgo his kavod to stop the machlokes. Furthermore, we find in Yoma 3 that according to R. Yoshiah the trumpets had to be paid for by Moshe himself - why would something that is there to honor the king have to be paid for by the king?
Rav Moshe Feinstein explains that Moshe's status as king was very different than a regular king. He wasn't formally appointed as king by klal yisroel or by Hashem. Actually Moshe says in parshas ba'haloscha כי תאמר אלי שאהו בחיקך כאשר ישא האומן את היונק and Rashi comments that Moshe had to take responsibility over klal yisroel and tolerate their nasty comments with very thick skin. This behavior is very not king-like, rather very shepherd-like (although Rambam in Melachim 2:6) explains that a Jewish king is essentially a shepherd, that is only to do the actions of a shepherd but not to tolerate the lack of respect). Therefore, Moshe' status as king resulted from his mastery of Torah. As Chazal say מאן מלכי? רבנן. When one Torah scholar stands above the rest in his generation, he has status as king in the sense that all are subject to his p'sak. Since Moshe's status as king wasn't by appointment, rather from the fact that he was the greatest Torah scholar - משה רבינו, Hashem wanted trumpets blown to honor him, but didn't want him to receive benefit from his Torah and therefore insisted that Moshe pay for the trumpets himself.
With this Rav Moshe explains that gemara in Kiddushin 33b says that one must stand for a Nassi until he is no longer visible as we see that they stood for moshe until he reached his tent (parshas ki tisa) - Rashi comments: Moshe was a Nassi. The Mitzpeh Eisan asks that Moshe was more than a Nassi, he was a king. How can we learn from Moshe that this halacha even applies to a Nassi? Rav Moshe explains that Moshe's status as king came from his Torah. The greatest Torah scholar of the generation is the Nassi. Although Moshe was able to rise above the standard title of Nassi to be king because he was רבן של כל ישראל, the level of kavod owed to him was that of a Nassi since the source of his status of kavod is the same as a Nassi. That is why Moshe was able to be mochel on his kavod.
It seems to me that Rav Moshe Feinstein's approach is also found in the Ibn Ezra in Devorim (33:5) on the pasuk of ויהי בישרון מלך where he writes:
הוא משה, ששמעו ראשי עם התורה מפורשת מפיו, והטעם כי הוא היה כמלך והתאספו אליו ראשי השבטים
The Ibn Ezra understands that the king refers to Moshe because he taught Torah to klal yisroel. With the approach of Rav Moshe Feinstein that regarding kavod Moshe's status was limited to that of a Nassi and he was able to be mochel and forgo his honor, we can understand rashi in parshas yisro. Rashi explains the pasuk that says Aharon and the elders joined Yisro to eat bread - where was moshe? Moshe was standing and serving. How can Moshe be mochel on his kavod to serve Yisro since a king can't be mochel on his kavod? Clearly, regarding the kavod due to Moshe his status was that of a Nassi, not a king.