I don't agree with the traditional view that wooden ships can't be more than 200 feet long. I think 400 feet is definitely possible. Ancient Greeks of Hellenistic era did in fact build wooden prestige ships 400 feet long, supported and kept hog free with a ingenious system of pulleys tensioning highly tensioned hawsers. Some of those ships had a crew of 6000.
The 200 foot limit experienced by western wooden vessels from post-Roman era to beginning of 1800 were due to the lack of 4 major structural refinements:
1. Diagonal framing
2. Internal transverse strength bulkheads
3. Internal longitudinal strength bulkeads
4. Internal tensioned cables for keeping the deck in compression.
Each of these refinements were possible in a wooden ship constructed using techniques available in 1400. Their absence from western ships before 1800 was largely a result of design conservatism, not insurmountable technical challenge.
Internal tensioned cables for keeping the deck in compression was a
technique well known to the Greeks and Romans, but largely forgotten in
the west after the middle ages. This had enabled the largest Greek
and Roman wooden warships to reach well over 400 feet long.
Internal transverse strength bulkheads and Internal longitudinal strength bulkeads never came to large ocean going wooden ships of the western world. They only made their apperence in westen ships after iron has taken over as the main structural material. But they were possible in wooden vessels. The Chinese did have both Internal longitudinal strength bulkeads, and Internal longitudinal strength bulkeads in their large wooden junks. Modern steel vessels derive a great deal of their structural strength from internal bulkheads.
Diagonal framing came to western wooden ships only in 1807, when Robert
Seppings, surveyor of the Royal Navy, introduced the concept. This
immediately allowed a great expansion in acceptable length. By 1840,
largely wooden first rate ships of the line were already approaching
8000 tons and 300 feet in length.
So based on this, I think it is within the realm of engineering possibility to build 400 foot long mostly wooden sea-going vessels in 1400s. Whether the Chinese actually did do so we may never know for sure. But to my knowledge there is nothing that says it really can not be done using 1400 technology.
What I do find impossible are the current reconstruction of what hypothetical chinese 400 footers would look like. These reconstructions were clearly not done by thoughtful naval architects. The broad, shallow hull depicted in most reconstructions could not have been very weatherly. They would have sagged amazingly to leward when sailing in a cross wind. They would never be able to beat off a lee shore should they be caught in any storm. These reconstructions do not represent highly sea worthy vessels, in my opinion. They do not depict ships that could survive a Monsoon season in the Indian ocean or a typhoon season in the China sea. Any reasonable seawothy vessel must either be far more deep drafted, and narrower, or possess a very large laboard.