There are a few records of Chinese Muslims making the trip, though allegedly Zheng He, perhaps the most famous Muslim in pre-modern China, never made it himself despite being in the area in the 1400s. His father and grandfather allegedly did make the trip, though in most sources where this is referenced, for his father it's based on him having the name 馬哈吉 ma ha ji, Hajji Mǎ. Another source says ma ha ji is a transliteration of "Muhammad", which I find questionably.

In general, for the dates you gave, there aren't too many records of Chinese Muslims taking the trip. The great Chinese scholars of Islam didn't really show up until the early 17th century (Wang Daiyu, Liu Zhi et al), and there was a bit of a resurgence after their works. There are some well known cases starting in the 19th to early 20th century. But, the Islamic population in China wasn't linguistically or ethnically homogeneous at the beginning of the time frame, leaving a lot of variables, including in terms of what would have been recorded in extant Chinese sources. The likelihood of going may vary considerably based on which part of China you're starting in.

If you can wait a couple days I can check older Chinese sources and see what I can dig up, but I won't have access until Monday.

Follow-up question: it was my understanding that in more distant locations, a large portion of the Muslim population were upper-class converts who tried to gain more ties to traders; what exactly would be the average wealth of a Muslim in aforementioned countries in relation to the general populace?

Also, good question OP. I hope someone knowledgeable can answer it.