This is not a solution, but it explains why it's not easy to find apps that support moving windows between spaces.
According to the developer of the open source Rectangles App, a keyboard-based window organizer, "Apple doesn't provide public APIs for Spaces. If at some point they do, I'll be glad to to revisit this [feature request]."
Apps that do provide this feature use a private API of Apple's, which is not supported or documented by Apple. Amethyst is an open source app that supports the feature (mentioned in another answer). If you're curious, it seems the code that performs moves a window from one space to another is in Window.swift:
// A method of Window:
final class AXWindowID: Hashable, Codable {
// ...
func move(toSpace spaceID: CGSSpaceID) {
let currentSpace = CGSGetActiveSpace(CGSMainConnectionID())
let ids = [cgID()]
CGSRemoveWindowsFromSpaces(CGSMainConnectionID(), ids as CFArray, [currentSpace] as CFArray)
CGSAddWindowsToSpaces(CGSMainConnectionID(), ids as CFArray, [spaceID] as CFArray)
if UserConfiguration.shared.followWindowsThrownBetweenSpaces() {
focus()
}
}
}
Ctrl
+<-
and theCtrl
+->
that is the source of grief, know that you can change the shortcut key for moving spaces. It's under System Preferences -> Keyboard -> Shortcuts -> Mission Control