To set any response header, you should overwrite OnPreHTTP method in your CSP Page class.

 Class User.Page Extends %CSP.Page
{

ClassMethod OnPage() As %Status
{
  &html<<html>
<head>
</head>
<body>>
  ; To do...
  &html<</body>
</html>>
  Quit $$$OK
}

/// Event handler for <b>PreHTTP</b> event: this is invoked before
/// the HTTP headers for a CSP page have been sent. All changes to the
/// <class>%CSP.Response</class> class, such as adding cookies, HTTP headers,
/// setting the content type etc. must be made from within the OnPreHTTP() method.
/// Also changes to the state of the CSP application such as changing
/// %session.EndSession or %session.AppTimeout must be made within the OnPreHTTP() method.
/// It is prefered that changes to %session.Preserve are also made in the OnPreHTTP() method
/// as this is more efficient, although it is supported in any section of the page.
/// Return <b>0</b> to prevent <method>OnPage</method> from being called.
ClassMethod OnPreHTTP() As %Boolean [ ServerOnly = 1 ]
{
  Do %response.SetHeader("X-MyHeader", "some info")
  quit 1
}

}

In the first implementation, I tried to actually build the tree. But missed something, and got some duplications in the lowest branches. Then using the same tree trying to solve second part, I found more than one unbalanced branches and a long time had not noticed how it could be until I noticed duplications. Then I removed this way, and first part becomes much simpler if just search node which does not have parents. In the second part, you actually already have a tree when you know when it started from the first part.

Looks like just some simple implementation for Long Pulling requests.

But how about getting not just a progress but how to get some data before task finished. 

And also, I see beg security Issue, when I can get information from any other process. You use TaskId directly from the request like you trust everybody. And also easy to get SUBSCRIPT error.

BTW: do you suppose to acept someone's answer? Looks like it is mostly just discissing topic.

For current process

USER>f fmt="enuw","rusw","current","" do ##class(%SYS.NLS.Format).%New(fmt) w !,fmt,?10,$zd($h,11),?15,$zd($h,12)
 
enuw      Wed  Wednesday
rusw      Сре  Среда
current   St   středa
          Wed  Wednesday

Or for all new processes, without restart

%SYS>write $zd($h,12)
Wednesday
%SYS>Set ^SYS("NLS","Config","LocaleFormat")=1
 
%SYS>write $zd($h,12)
Wednesday
%SYS>Do Locale^NLSLOAD("rusw")
 
%SYS>write $zd($h,12)
Среда