You seem to misunderstand centrism to such an extent that you're essentially attacking a strawman. Centrism isn't an imaginary middle-point on a spectrum between opposing ideologies. It's essentially just a pragmatic selection of various political ideas, depending on the person and their situation.
Most of the self-described "radical centrists" I've met aren't attempting to perform any sort of ideological balancing act between left and right, it's just that they simultaneously hold a particular mix of ideas from both the liberal & conservative parties in such a way as to never be able to fully side with Republicans or Democrats. They find themselves split by a zig-zagging line across so many different issues that they must reject both major parties.
For example, someone who deeply supports abortion rights and LGBTQ marriage, but also feels strongly about the 2nd Amendment might describe themselves as a centrist. Those are all strongly held beliefs and none of them occupy any middle ground. It's not intellectually lazy or morally bankrupt to hold a mix of ideas that don't fit neatly into either major party.
This is how I've always seen it as well, though I consider myself independent.
It's funny the issues you mention are commonly held by quite a few people I know, myself included. "Why can't the gay couple up the street get married, while smoking weed and shooting off some rifles?" is how I describe my views.
I've definitely noticed that the amount of people I meet with views like that have been a little rarer lately.
How does a party of such people organize? What policy positions could they hold on abortion, lgbtq rights, and gun rights that will lead to wide appeal?
That is the million dollar question. But perhaps quantitative research would show that there is a golden balance, where a particular centrist set of policies actually can attract a significant set of voters?
Most of the self-described "radical centrists" I've met aren't attempting to perform any sort of ideological balancing act between left and right, it's just that they simultaneously hold a particular mix of ideas from both the liberal & conservative parties in such a way as to never be able to fully side with Republicans or Democrats. They find themselves split by a zig-zagging line across so many different issues that they must reject both major parties.
For example, someone who deeply supports abortion rights and LGBTQ marriage, but also feels strongly about the 2nd Amendment might describe themselves as a centrist. Those are all strongly held beliefs and none of them occupy any middle ground. It's not intellectually lazy or morally bankrupt to hold a mix of ideas that don't fit neatly into either major party.