Merge by condition and approximate matching in Power Query

I don't know if that's exactly what you're looking for (in the sense that being simple and "better" at the same time isn't common).
At least the functions you mentioned and which, for some reason, did not satisfy you are not used.

edit:

This solution assumes that the Change date manager table is sorted in ascending order.
Otherwise it can be easily adapted to the generic case.

let
    OrderTable = Excel.CurrentWorkbook(){[Name="OrderTable"]}[Content],
    ManagerTable = Excel.CurrentWorkbook(){[Name="ManagerTable"]}[Content],
    Custom1 = let
                 mt=Table.Group(
                                ManagerTable,
                                "Client",
                                {"n",each Table.ToRows(Table.Sort(_,{"Manager Change Date",1}))}
                               )
              in
                 Table.AddColumn(
                                 OrderTable,
                                 "Manager",
                                 each let
                                         a=mt{[Client=[Client]]}?[n]?
                                      in
                                        if a=null then "Mng.1"
                                        else List.Skip(a,(x)=>x{1}>[Order Date]){0}?{2}? ??"Mng.1"
                                )
in
    Custom1

Could you elaborate on the concept expressed in the following sentence?

"I have faced to solutions in the net, with Full outer merge - Conditional column - Group by - Fill down, but they aren't too good. Let's try to finde more simple and better one."