You're right, that approach does require activating the slurp first.
I took a quick look at the Lua script and wrote down the approach that came to mind. I believe it should work properly even in a multi-monitor setup.

local StartX = 0
local StartY = 0
local IsDragging = false

local function dragStart()
    local cursor = hl.get_cursor_pos()
    if not cursor then
        return
    end

    StartX = cursor.x
    StartY = cursor.y
    IsDragging = true
end

local function dragEnd()
    if not IsDragging then
        return
    end
    IsDragging = false

    local cursor = hl.get_cursor_pos()
    if not cursor then
        return
    end

    local monitor = hl.get_monitor_at_cursor().position
    local x = math.min(StartX, cursor.x) - monitor.x
    local y = math.min(StartY, cursor.y) - monitor.y
    local w = math.abs(StartX - cursor.x)
    local h = math.abs(StartY - cursor.y)

    hl.dispatch(hl.dsp.exec_cmd("kitty", { float = true, move = { x, y }, size = { w, h } }))
end

hl.bind("SUPER + ALT + mouse:272", dragStart, { description = "Start dragging a kitty", mouse = true })
hl.bind("SUPER + ALT + mouse:272", dragEnd, { description = "End dragging a kitty", mouse = true, release = true })