What bugs me with the idea that polygamy and polyamory are two completely different things that just happen to intersect is that to me polygamy is a subscategory of polyamory, and it can be done wrong, just like poly can be done wrong and lead to trouble.
But to me, polyamory means the ability to be in love with more than one person at a time, or the practice of having more than one partner at a time. It's not a "movement", it's a relationship orientation. And as much as people want to include "equality of the sexes" and things like that into the definition, I disagree, unless we redefine monogamy to exclude the possibility of inequality between the sexes as well.
Some polyamorous, non-polygamous relationships aren't egalitarian. Some are one way (you can date women but not men/ I can date other people but you can't) and everyone involved is fine with the decided rules, as much as it might seem unfair from the outside.
Religious polygyny seems unfair from the outside to a lot of people, but I entirely believe that it has the potential to be done right, with the consent and knowledge of everyone involved, which is what polyamory is all about.
The fact that there can be abuse in polygamy doesn't make it a different category in my opinion, as there can be abuse in all relationships and that doesn't cause them not to be considered relationships anymore.
Polyamory is about having more than one partner. Polygamy is about having a marriage-like relationship with more than one partner. Therefore polygamy is a form of polyamory, just like monogamous marriage is a form of monogamy, and both polyamory and monogamy are types of relationships.
If you take your all arguments and replace "polyamory" with "monogamy" and "polygamy" with "monogamous marriage", I'm sure you can see that "monogamy and monogamous marriage are two different entities that just happen to intersect" sounds wrong. (Unless you think it doesn't because forced marriages exist and it somehow makes it nonmonogamous, and then I'd love to hear your reasoning).