The problem being we have no extant items from the 15th century matching the description. We have inventory entries, and then we have some illustrations of what seem to be curious forms of the padded jack in the Beauchamp pagent and elsewhere. Outside of a badly degraded late 15th/early 16th century padded jack in the UK, and what are possibly two examples in Sweden or Germany, we have nothing extant to go by, and of course they aren't stuffed with horn.

What seems to be shown in the Beauchamp pagent, worn by some footsoldiers is a vertically stitched jack, with a series of protruding nail heads in vertical collumn centerally located between the vertical stitching. This would indicate to me that the plates that the nails presumably hold do not overlap in every direction, in the manner of a brigandine. They might overlap like shingles vertically, but I suspect that they might not as well, or at least nopt overlap significantly. At least were I to try to make a speculative reconstruction, looking at the spacing of the nail heads, I would not be expecting any significant overlap.

The Fastolf inventory also mentions 'jacks stuffed with mail', the Howard books mentions a mail andd cloth defence. In these cases, what is likely given the constructiion of mail, the examples seen in the mideast, and the mail coif lining (presumed) extant from the late 13th century, that a mail garment is given layers of padding andf a cover, rather than being literaly a jack with links or sheets of mail stuffed inbetween the stitching, so I don't think what we see in the Beauchamp pagent is one of these, more likely a jack reenforced with horn or plate.

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The C16th Jack is essentially a hybrid of the earlier jack and pairs of brigandines. Basically pairs of Brigandines have an outer layering of cloths with overlapping plates riveted to them, but no lining. Typically the plates are riveted using multiple nails in clusters (groups of 3 being 'classic'). In contrast the Jack was a garment with an outer, and a lining and some form of protection between ... sometimes tow (linen) sometimes linen cloth sometimes cotton wadding.

However by the C16th, and plenty of examples survive, Jacks are seen made with the outer and lining cloths but between them are small metal plates stitched in place, other with a single attachment.

Since 'stuffed' appears to have been used primarily to mean 'lined' it is not a massive leap of faith to see the horn working in a similar manner.

The problem is that without the evidence ... and as has been said there is hardly any for the standard cloth Jack let alone a 'stuffed with horn' Jack ... quite what form these horn 'plates' took (if that is what they were) and how they were positioned is open to serious debate.

The pattern of the stitching in the C16th Jack (typically a diamond stich) doesn't appear very often in illustrations of C15th jacks and so we can't use that comparison.
Also we know that the shape and rivting 'style; for the construction of a pair of Brigandines changed as the C15th progressed and into the c16th. So we know that these types of armour were very susceptible to stylistic change.

If I were to hazard a guess I'd also go with the Beauchamp styling as this has never been properly explained, and the rigid style would fit well with boning. But here lies another problem ... was the horn actually defensive (as per the plates in pairs of brigandines) or constructional. I think defensive the most probably judging by the context ... but it needs to be considered.

So in summary ... to answer your question ... no one knows. My personal preference would be butted plates stitched through as per C16th jacks. The plates are not visible but internal. But if you do make one, you need to make the stitch pattern fit known styles for Jacks.

Good Luck.