If you need to use Web-Service rather than API and edit it SharePoint Designer, would you please try this:
· Migrate your web-page logic to a UserControl and then package with a webpart, after that you can use the webpart in SharePoint Desinger,
but this also need some deployment on server.
· Also, you can use J-Query for webservice in SharePoint Designer, as suggestion in this thread, and you only need to re-write the btnSubmit method,
replace it to client method using J-Query.
Is the name tasks also the actual listname in the url? i.e. http://siteurl/lists/tasks? is the list in a subsite and are you using the service under the site-collection?
IF the list is in a subsite the use http://sitecollectionurl/subsite/_vti_bin/lists.asmx as the Service url, otherwise the lists.asmx will try to find the tasks list in the rootweb instead of the subsite.