Are you using Git for your source control? If so, you may want to start a new branch and work in it before doing any major re-factoring.
To start, I would try to find a small part of the application that you feel would be possible to re-factor in an hour or so. Before changing anything, I would load up the app locally in your browser and navigate to the portion that is dependent upon the code you're going to re-factor. Then I would re-factor things in as small a chunk as possible, constantly checking in the browser to make sure things still work properly. This is a rather bastardized approach to test driven development, but it can be quick and effective.
> The architecture of it all is very monolithic; based on our plans for the future business development, quite a few parts should be decoupled and made more independent of each other.
As a side note.. This type of thing I have seen way too much of in my time in the industry. It's very easy to get carried away and over-engineer a solution. I've found it's best to create a solution that solves only the problems you currently need solved. It's always easier to go back and extend while re-factoring than it is to try to re-factor a giant-freakin'-thing after the fact.