Converting a form from html/php to wordpress

I’m converting a form from an old html login page to WordPress login page. If I want a form that calls a POST to, say, Infusionsoft or any other external url, I found that I can literally drop the html into the Text and it will submit the data…until an error is reached.

The error conditions are handled at the post action side of the transaction through an action called “login.php”. I pretty sure it’s out of my hands at that point.

What can I do to manage this form at the WordPress site?

I tried Gravity Forms but they’re not so good making a second post without much code, they just a post to themselves in storing the fields locally.

Any ideas are welcome.