This gist shows how could one use Kudu api/zip in combination with api/vfs to deliver archive outside of web app webroot and overcome hardcoded request timeout

deliverZipArchive.ps1

$unicornFilesZip = "c:\temp\unicorn.zip";
$indicatorFileName = "z.z." + "$(buildNumberVar)" + ".txt";
$scmTargetPath = "C:\home\N";
$unicornFolder = Split-Path $scmTargetPath -Leaf;

function Get-HttpBasicAuthHeader
{
    Param(
        [Parameter(Mandatory=$true)]
        [string]$UserName,

        [Parameter(Mandatory=$true)]
        [string]$Password
    )

    $pair = [string]::Format("{0}:{1}", $UserName, $Password)
    $bytes = [System.Text.Encoding]::ASCII.GetBytes($pair)
    $base64 = [System.Convert]::ToBase64String($bytes)
    $basicAuthValue = [string]::Format("Basic {0}", $base64)

    return @{ Authorization = $basicAuthValue }
}

Write-Output "Deploying Unicorn files";
$Headers = @{};
$Headers += Get-HttpBasicAuthHeader -UserName '$(scmUserName)' -Password '$(scmPasswrod)';
$kuduApiUrl = "https://$(webAppName).scm.azurewebsites.net/api/zip/$($unicornFolder)";
$kuduVfsUrl = "https://$(webAppName).scm.azurewebsites.net/api/vfs/$($unicornFolder)/$($indicatorFileName)";

$checkFileRetryCount = 0;
$sleepTimeSeconds = 30;
$maxWaitTimeMinutes = 30;
# we will wait maximum for $maxWaitTimeMinutes
$maxRetryCount = ($maxWaitTimeMinutes * 60) / $sleepTimeSeconds;


# using Zip Api to deploy Unicorn files - it is much faster then deploying small files via MsDeploy
Write-Output "Deploying to $kuduApiUrl via zipdeploy Unicorn files in archive $unicornFilesZip";
Invoke-WebRequest -Uri $kuduApiUrl -Headers $Headers -InFile $unicornFilesZip -ContentType "multipart/form-data" -Method Put -UseBasicParsing -ErrorAction SilentlyContinue -ErrorVariable errorVar; 

# wait, until indicator is not present there
do {
    $request = $null;
    $result = $false;
    $request = Invoke-WebRequest -Uri $kuduVfsUrl -Headers $Headers -UseBasicParsing -ErrorAction SilentlyContinue -ErrorVariable errorVar;
    if ($null -ne $request -and $request.Status.Code -eq 200) {
        $result = $true;
    }
    $message = "Check file is not present at $($kuduVfsUrl). Current try count is $($checkFileRetryCount).";
    if ($checkFileRetryCount -ge $maxRetryCount) {
        Write-Output $message" Cancelling...";
        exit -1;
    }
    if ($result) {
        Write-Output "Check file is present at $($kuduVfsUrl). Current try count is $($checkFileRetryCount).";
    }
    else {
        Write-Output $message;
    }
    Start-Sleep -Seconds $sleepTimeSeconds;
    $checkFileRetryCount++;
} while ($result)