To get this out of the way first: In addition to the one mentioned earlier, another reason not to use plugins for operations-critical aspects of the site is because installing another plugin, or another plugin being upgraded, might interfere with the critical plugin. As an example, older versions of Woo Commerce (I don’t have information about latest versions) aren’t compatible with Insert PHP.
For your multi-page forms, my inclination (although realizing I don’t have all the information at hand to make a positive recommendation) is to suggest creating separate templates for the forms. Although I have created custom templates, it’s futzy and time-consuming work for me and I would be pleased if, should you decide to go that route, you could find someone else to do it for you.
Note that forms with method GET is undesirable because whether or not GET works depends on permalinks setting. Someone changing the permalinks setting could disable the forms site-wide.
Another way to implement your multi-page forms is to use Ajax. This is more along my line of expertise and something I’m willing to help you with.
One line of JavaScript can pull the forms into a page. Ajax is used to submit the forms. When one form page is submitted, it’s replaced with the next form page. PHP scripts on the server deliver the forms and handle the form submissions.
Downside: Form pages appear at the same URL, making it impossible for the user to click the “back” button for the pervious page (although a “back” link could be provided).
Upside: Form-spamming robots are unlikely to find the form or use it successfully.
Will