As noted in some of the comments, newer versions of the HTTP specification have clarified this somewhat. Per Section 4.3.4 of RFC 7231:
An origin server that allows PUT on a given target resource MUST send
a 400 (Bad Request) response to a PUT request that contains a
Content-Range header field (Section 4.2 of [RFC7233]), since the payload
is likely to be partial content that has been mistakenly PUT as a full
representation. Partial content updates are possible by targeting a
separately identified resource with state that overlaps a portion of the
larger resource, or by using a different method that has been specifically
defined for partial updates (for example, the PATCH method defined in
[RFC5789]).
Unfortunately, the discussion of the range headers which occurs in RFC 7233 focuses more or less entirely on GET requests, and RFC 5789 defines almost nothing about PATCH except that it is specifically not required to transmit the entire content (but is allowed to), nor is it required to be idempotent (but is allowed to be).
The bright side is that because PATCH is so loosely defined, it does accommodate the approach given in an answer to a related question (https://stackoverflow.com/a/6711496/7467189): just change "PUT" to "PATCH". While there is no requirement that a server interpret a PATCH request with a Content-Range header this way, it is certainly a valid interpretation, just not one that can be relied upon from arbitrary servers or clients. But in cases such as the original question, where control of both ends is available, it is at least an obvious approach and does not violate the current standards.
One additional consideration is that the Content-Type should express whatever is being transmitted, rather than the content type of the entity as a whole (the RFC gives some examples in this regard). For content that is being "patched" in arbitrary chunks this would imply application/octet-stream, although there are scenarios where the client and server might be more content-aware and opt to send patches as entities which have a more specific definition (e.g. single pages of a multi-page image format).