If you're looking to simply convert timezone codes to the UTC offset, I'd setup a simple utility that returns the desired string based on a case statement.

Something like:

ClassMethod DisplayTimezoneToUTCOffset(pInput as %String) As %String{
    Quit $CASE($ZCONVERT(pInput,"U"),
    "CEST":"+02:00",
    "CET":"+01:00",
    "BST":"+01:00",
    :"")
}

If you then want to build the entire string, you could do similar to above for the months, and then have the following:

Class Demo.Utils.ExampleUtils.TimeConvert
{
ClassMethod DisplayDateTimeToLiteral(pInput as %String) As %String{
    // Deconstruct the input string into it's logical parts.
    // Variables starting d are "display" values that will be converted later.
    Set DayOfWeek = $P(pInput," ",1) //Not used
    Set dMonth = $P(pInput," ",2)
    Set Day = $P(pInput," ",3)
    Set Time = $P(pInput," ",4)
    Set dTimeZone = $P(pInput," ",5)
    Set Year = $P(pInput," ",6)

    //Return final timestamp
    Quit Year_"-"_..DisplayMonthToLiteral(dMonth)_"-"_Day_" "_Time_..DisplayTimezoneToUTCOffset(dTimeZone)

}

ClassMethod DisplayTimezoneToUTCOffset(pInput as %String) As %String{

    Quit $CASE($ZCONVERT(pInput,"U"),
    "CEST":"+02:00",
    "CET":"+01:00",
    "BST":"+01:00",
    :"")
}

ClassMethod DisplayMonthToLiteral(pInput as %String) As %String{

    Quit $CASE($ZCONVERT(pInput,"U"),
    "JAN":"01",
    "FEB":"02",
    "MAR":"03",
    //etc. etc.
    "JUL":"07",
    :"")
}

}

Which then gives the following:

Hi Nezla.

As the URL starts out as "ac1.mqtt.sx3ac.com", suggesting that the API is using MQTT, is the %net.httprequest adapter the right way to go?

I think it'd be good to take a look at Using the MQTT Adapters to see how the adapter can be used if you haven't already.

Have you tried adding backticks to your double-quotes to escape them?

PS C:\Users\Colin\Desktop> irissession healthconnect -U user 'Say^ImplUtil(`"Your String Here`")'