Note: it doesn't prevent the moving to the target space for the window; but it does instantly revert you to the original space after the window has been moved to the target space.
Note: Requires "Switch to desktop..." shortcut keys to be enabled in the Mission Control section of the Keyboard Shortcuts section of the Keyboard System Settings. There may be a way to more elegantly switch to a space, programmatically, but having trouble finding it. Seems Spaces scripting is very un-developed by Apple.
Note: the delays included in the script may need to be adjusted for your machine to achieve optimal performance.
Instructions: For whatever trigger you've selected, after the "Move Window to Desktop X" action, create a "Run Apple Script" action, with the following AppleScript code:
tell application ¬
"System Events" to tell process ¬
"WhichSpace" to set WhichSpaceDump to (title of menu bar items of menu bar 1)
set SpaceNum to item 1 of WhichSpaceDump
delay 0.1
--Delay switching back to original space until the BBT menu has been activated and resulted in a change of space
tell application ¬
"System Events" to tell process ¬
"WhichSpace" to set WhichSpaceDump to (title of menu bar items of menu bar 1)
set CurrentSpaceNum to item 1 of WhichSpaceDump
repeat until CurrentSpaceNum is not SpaceNum
tell application ¬
"System Events" to tell process ¬
"WhichSpace" to set WhichSpaceDump to (title of menu bar items of menu bar 1)
set CurrentSpaceNum to item 1 of WhichSpaceDump
delay 0.1
end repeat
delay 0.1
if SpaceNum is "1" then
delay 0.1
tell application "System Events" to key code 18 using {control down}
end if
if SpaceNum is "2" then
delay 0.1
tell application "System Events" to key code 19 using {control down}
end if
if SpaceNum is "3" then
delay 0.1
tell application "System Events" to key code 20 using {control down}
end if
if SpaceNum is "4" then
delay 0.1
tell application "System Events" to key code 21 using {control down}
end if
if SpaceNum is "5" then
delay 0.1
tell application "System Events" to key code 23 using {control down}
end if
if SpaceNum is "6" then
delay 0.1
tell application "System Events" to key code 22 using {control down}
end if
if SpaceNum is "7" then
delay 0.1
tell application "System Events" to key code 26 using {control down}
end if
if SpaceNum is "8" then
delay 0.1
tell application "System Events" to key code 28 using {control down}
end if
if SpaceNum is "9" then
delay 0.1
tell application "System Events" to key code 25 using {control down}
end if
if SpaceNum is "10" then
delay 0.1
tell application "System Events" to key code 29 using {control down}
end if
if SpaceNum is "11" then
delay 0.1
tell application "System Events" to key code 18 using {control down, option down}
end if
if SpaceNum is "12" then
delay 0.1
tell application "System Events" to key code 19 using {control down, option down}
end if
if SpaceNum is "13" then
delay 0.1
tell application "System Events" to key code 20 using {control down, option down}
end if
if SpaceNum is "14" then
delay 0.1
tell application "System Events" to key code 21 using {control down, option down}
end if
if SpaceNum is "15" then
delay 0.1
tell application "System Events" to key code 23 using {control down, option down}
end if
if SpaceNum is "16" then
delay 0.1
tell application "System Events" to key code 22 using {control down, option down}
end if
unless I miss something, this can't do what the "Only Move Window, Do NOT Switch To Space" option did. It moved a window to a different space without actually switching to that space. (Unfortunately Apple blocked that on current macOS)
The standard move window to space actions should still work in BTT.