Here's a sample, using %ToDynamicObject (2016.2+):

Class DC.CustomJSONSample extends %RegisteredObject
{
Property myProperty As %String [ InitialExpression = "hello" ];

Property other As %String [ InitialExpression = "world" ];

/// Rename myProperty to custom_property_name
Method %ToDynamicObject(target As %Object = "", ignoreUnknown = 0) [ ServerOnly = 1 ]
{
	Do ##super(.target,.ignoreUnknown)
	Do target.$set("custom_property_name",target.myProperty,target.$getTypeOf("myProperty"))
	Do target.$remove("myProperty")
}

ClassMethod Run()
{
	Set tObj = ..%New()
	Write tObj.$toJSON()
}

}

Output:

SAMPLES>d ##class(DC.CustomJSONSample).Run()
{"other":"world","custom_property_name":"hello"}

For other discussions with solutions/examples involving %ToDynamicObject, see:
https://community.intersystems.com/post/json-cache-and-datetime
https://community.intersystems.com/post/create-dynamic-object-object-id

Also see the class documentation for Security.Applications:

[quote]

Bit 2 = AutheK5API
Bit 5 - AutheCache
Bit 6 = AutheUnauthenticated
Bit 11 = AutheLDAP
Bit 12 = AutheLDAPCache
Bit 13 = AutheDelegated
Bit 14 = LoginToken
Bit 20 = TwoFactorSMS
Bit 21 = TwoFactorPW

[/quote]

The problem is that REST uses IO redirection itself, and OutputToStr changes the mnemonic routine but doesn't change it back at the end.

For a great example of the general safe approach to cleaning up after IO redirection (restoring to the previous state of everything), see %WriteJSONStreamFromObject in %ZEN.Auxiliary.jsonProvider.

Here's a simple approach that works for me, in this case:

set tOldIORedirected = ##class(%Device).ReDirectIO()
set tOldMnemonic = ##class(%Device).GetMnemonicRoutine()
set tOldIO = $io
try {
	set str=""

	//Redirect IO to the current routine - makes use of the labels defined below
	use $io::("^"_$ZNAME)

	//Enable redirection
	do ##class(%Device).ReDirectIO(1)

	if $isobject(pObj) {
		do $Method(pObj,pMethod,pArgs...)
	} elseif $$$comClassDefined(pObj) {
		do $ClassMethod(pObj,pMethod,pArgs...)
	}
} catch ex {
	set str = ""
}

//Return to original redirection/mnemonic routine settings
if (tOldMnemonic '= "") {
	use tOldIO::("^"_tOldMnemonic)
} else {
	use tOldIO
}
do ##class(%Device).ReDirectIO(tOldIORedirected)

quit str

It would be cool if something like this could work instead:

new $io
try {
	set str=""

	//Redirect IO to the current routine - makes use of the labels defined below
	use $io::("^"_$ZNAME)

	//Enable redirection
	do ##class(%Device).ReDirectIO(1)

	if $isobject(pObj) {
		do $Method(pObj,pMethod,pArgs...)
	} elseif $$$comClassDefined(pObj) {
		do $ClassMethod(pObj,pMethod,pArgs...)
	}
} catch ex {
	set str = ""
}

quit str

But $io can't be new'd.

You could map the package containing the class related to that table using a package mapping, and the globals containing the table's data using global mappings.

You can see which globals the class uses in its storage definition - since the entire package is mapped, it might make sense to add a global mapping with the package name and a wildcard (*).

After taking those steps, you can insert to the table the way you usually would, without any special syntax or using zn/set $namespace.

There was a similar question and answer at https://community.intersystems.com/post/how-include-dynaform-custom-task-form-ensemble-workflow that might be helpful.

In short, the simplest solution (and possibly the only one) would be to put the Zen page in an <iframe> in a CSP page that EnsLib.Workflow.TaskRequest.%FormTemplate points to.

I really would recommend creating a %All namespace (if there isn't already one), via %Installer or something that works similarly.

One projects on the intersystems-ru github, Caché Web Terminal, has the same requirement (use from any namespace); this class might be helpful for reference: https://github.com/intersystems-ru/webterminal/blob/master/export/WebTerminal/Installer.xml. It doesn't actually use %Installer, so configuration changes are implemented in COS instead of being generated based on XML, but it works similarly.

Particularly, see methods CreateAllNamespace and Map/UnMap. You should be able to adapt these without too much effort. If your code coverage project eventually has a UI, then the web application setup method will be useful too (for simple installation).