I’m sorry for this late answer, but even if it’s too late, I’m still hoping to help others who ask the same question.
Generally, when a kanji has more than one reading, there is a trick to knowing which one to use, and it’s not completely arbitrary. Often, one reading will have a slightly different semantic meaning than the other, such as in 図 (“zu” reading used for diagrams, “to” for plans) and 木 (“moku” for wood, “boku” for tree), or one reading will be more often used as a prefix and the other as a suffix, such as in 後 (“kou” when a prefix, and “go” as a suffix). Sometimes, one reading will be far more common in two-kanji compound words and the other far more common in greater-than-two-kanji compound words, like in the case of 大 (“tai” for two-kanji words, “dai” for greater than two). Most of time, people who claim that a kanji’s readings are completely arbitrary are wrong about that.
Native speakers are often unaware of these tricks to reading, because they speak and read their language on an unconscious level, without thinking too hard about it. Consider this, do you think deeply about the rules of English, or do you just use it naturally without thinking too much about it? Unless English isn’t your first language, you probably don’t think too hard about it. So, because people don’t think too much about their first language, you won’t always be able to find a native speaker who can reveal the trick to knowing. So, that’s probably why you couldn’t find an answer to this question from native speakers.
Now, to answer your question, the difference between “butsu” and “motsu” in 物 is that “motsu” has a nuance of a “valuable thing”, whereas “butsu” sounds neutral. Valuable things are frequently moved around as cargo, things that are edible to humans, treasures, or belongings. Even a word like “禁物 Kinmotsu = taboo” still fits in with the others, because taboo things are most often very tempting things that seem like useful assets. Logically, completely useless things are rarely ever taboo, because there is no temptation to use them in the first place.
However, there are words about valuable-sounding things that seem like they should use the “motsu” reading at first, like “薬物 yakubutsu = drug”, but then it turns out that they use the “butsu” reading instead. The reason for this is because 薬物 includes useless or addictive drugs as well as valuable ones, so the “butsu” reading is used in order to sound neutral and to avoid making a value-judgment.
To explain further, while most human-edible food product related words use “motsu”, “農産物 Nousanbutsu = Agricultural product/s” is an exception only because it’s based on a smaller word “産物 Sanbutsu = product/s.” Since some products can be faulty and useless or just poorly designed, the word uses a neutral “butsu.”
Another example, “人物 Jinbutsu = Personage” can be about any note-worthy figure or character, even an infamous person who didn’t do anything valuable and simply caused a lot of damage. This next one might seem like an exception, “名物 Meibutsu = Famous product”, but famous products are not necessarily valuable. For example, “pet rocks” are a famous product, but they are not a valuable product.
Here’s a few more examples that use “motsu”: “作物 Sakumotsu = Unprocessed edible crop product [literally ‘valuable thing that was made’, and what could be more valuable than life-giving food? Even bad-tasting edible food could save your life]” and “書物 Shomotsu = Valuable old book.”
Moreover, if something is of great personal importance to someone, then “motsu” is used. “荷物 Nimotsu = Luggage”, “貨物 Kamotsu = Cargo”, and “宝物 Houmotsu = Physical treasure; heirloom” are all about people’s treasured belongings, and things that are supposed to be handled carefully.
Another rule is that the “motsu” reading is not used when 物 comes first in a compound word; only when it comes last.
There might be a few genuine exceptions to these rules, but even if there are, it’s easier to learn the exceptions than to ignore the pattern. I’ve checked through words using the 物 kanji, and I don’t recall seeing any other exceptions. There definitely aren’t any words where the “motsu” reading of 物 comes first.
Also, I don’t have a source for this. This is just something that I noticed myself.
By the way, I was informed by native speakers that 書物 has a strong nuance of “old and valuable book”, which is why that word isn’t used for just any book. And I do have a source to back up this particular claim: https://ja.hinative.com/questions/15142040
I hope this helped.