There are quite a few services that should be able to solve this problem (turning a PDF into a web form and collecting signatures.) Here's a few of the services I'm aware of:
* https://www.hellosign.com/products/helloworks
* JotForm (https://www.jotform.com/help/433-How-to-Add-an-E-Signature-t...)
(I know about all these because I'm working on a PDF generation service for developers called DocSpring [1]. I'm also working on e-signature support [2], but that's still under development, and still won't be a perfect fit for your use-case.)