I think that there still may be a bit of disconnect in what we are discussing.
At this point, you don’t really have to do anything at all to avoid writing servlets. You always have the option of making liberal use of <% %> and <%= %> scripting tags to embed scads of Java code in your JSP, avoiding writing a servlet altogether.
Of course, at some point you will find that you have more stuff inside the scripting tags than outside, so your JSP is looking pretty much like your servlet would have.
I tend to steer clear of writing custom tags for business logic and use standard tag libraries for rendering and logic. This is because they are slightly convoluted to write and use, so I would rather just use the ones that have already been written by someone else.
The only “Beanify” part I can see in your business logic classes would be to make them accept and return bean classes in their arguments. For example, you may have a class called “PhoneDirectory” that has a method called “findPeople” which returns a collection of “Person” bean instances, each of which is a simple data carrier with methods like “getFirstName”, “getLastName”, “getPhoneNumber” and the like. This bit would likely be buried in a bit of scripting at the beginning of your JSP.
Now, when you want to actually display the people, you could take advantage of a preexisting custom tag library of things like looping constructs in order to loop through the array of Person bean objects, and use other tags to display individual instances of Person. (though you always have the option of using <% %> scripting everywhere, tags for looping and property display are much cleaner.)
See the Standard Tag Library or Struts for good tag libraries.
Again, the main point behind the standard JSP bean usage is to provide an easy way to stuff an instance of a bean into one of the four standard JSP scopes (page, request, session, application), as well as an easy means of automatically map the URL parameters to bean properties, as shown here. I prefer to use Struts instead for this task.