I very much agree with kcott above. Perl has several good web frameworks; perhaps the two most prominent right now are Mojolicious and Dancer2. (I'm partial to Dancer2 with Template Toolkit, myself.) Either will have the tools to help you separate your code from your design.

My advice: Don't rush. Spend a little time, even a few weeks, reading about them and looking at examples. Then start a clean, new project and start reconstructing your site the new way. You can create an unmaintainable mess even with good tools: fragile dependencies between objects, spaghetti callbacks to and from your templates. The time spent researching tools and getting familiar with them will pay. Same thing with testing.

Technology doesn't directly have much to do with how effective your site is. Dancer or Mojolicious won't directly lead to one more conversion (nor will most technology, despite what salespeople always say). People do that: you, as you gain more experience in your testing, or specialists that you might hire. Better technology makes it easier for you to do your jobs.