# [Red], 108 bytes

    func[n][i: s: 0 until[t: form i
    if(t > u: sort copy t)and(t < reverse u)[s: s + i n: n - 1]i: i + 1
    0 = n]s]

[Try it online!][TIO-jjb35768]

[Red]: http://www.red-lang.org
[TIO-jjb35768]: https://tio.run/##PYzBCgIhFEX3fsVdNkSgMBBI9RFtxUWMCg/qOTyfQV9vrmZ3OJdzJafxzClEU/wonbfAMZBH87DorPQO6lGqfECGyknxQJ9zFcVW9x90eXGa@gbJ3ywtoy9h1g1nENiDcYGL85KmccbiDo4tjl2IFWWqg@yB63q1bvwB "Red – Try It Online"

More readable:
-

    f: func [ n ] [
        i: s: 0
    	until [
    	   t: form i  
    	   if ( t > u: sort copy t ) and ( t < reverse u ) [
                s: s + i n: n - 1
           ]
    	   i: i + 1
    	   0 = n
    	]
    	s
    ]

A good opportunity to use `form` - `form i` is 5 bytes shorter than `to-string i`