That’s not possible without some custom coding.
There are really only two ways to do that:
1. Disable the default POST form submit and process the form via jQuery/AJAX so the page doesn’t have to reload. This would involve coding and loading custom jQuery code on the sign-up page, as well as adding a PHP function for the AJAX call to process and save the form data and return it to the jQuery script to display any messages/results.
2. You could put anchor tags on the page and have the form post action specify the anchor tag to go to. However, you would still need to modify the signup form plugin code with some kind of conditional check so that you know which signup form is being generated and which anchor tag it should go to. Right now the action for the forms is simply a blank screen since the plugin posts the form to the same page that you are already on (so that plugin users can use it on any page).
Neither solution is quick or simple, and would require quite a bit of custom programming. #1 is probably the preferred solution that is used more often these days. If you have a working budget, I’m happy to discuss privately what it might take to program that for you. But, since the free plugins are open source, if you or anyone you know has the programming skills, you can certainly give it a shot on your own.