Kyle,

Re. your last question...

Early constraints (start/finish on or after) are legitimately used in lieu of logic only when they represent the product of work that is truly external to the current project.  For example, if a construction contract includes installation of Owner-furnished material that the Owner promises (in the contract) to supply by the 1st of July, then an "Owner Material Ready" finish milestone with a FOA constraint of 01Jul'16 17:00 might be appropriate.  As a consequence, if the contractor has scheduled all his preparatory work to finish a week before arrival of the owner-furnished material, then those works have a week of float, and there will be no driving relationships between the contractor's preparatory works and the installation.  The "Critical Path" (or Longest Path) is truly and correctly truncated at the constrained milestone; it is what it is.  

I would suspect that many or most of your early constraints are used in place of logic (that is activities, durations and relationships, all internal to your project) that has simply not been defined.  You need to communicate with the stakeholders and determine what the missing logic is - i.e. why are these activities not starting at the beginning of the project?  Is the detail design and submittal process scheduled?  Is the material procurement and delivery process scheduled?  Is the mobilization and deployment of resources (manpower and equipment) scheduled?  I would not suggest using Start to Finish relationships (with or without lag) in any case. 

At the end of the day, your project might indeed only have one short "critical path" that is truncated by a legitimate early constraint, accompanied by a number of parallel near-critical paths.  You can use multiple float path analysis to define and display these.  (Here's something I wrote about MFP few months back: http://wp.me/p6CCB4-L).  The method Zoltan describes in his recent post is essentially a manual version of what P6 does automatically with MFP, though his description only exposes the first float path.

Good luck, tom

if this is the case you can change the value or the threshold to increase the definition of critical. Lets say that the least amount of float or longest path is 10 days. The default in the program for defining the critical path is set to 0 days.

To change the definition of critical based on the number of days of total float there are 2 places where you can do that one is at the project level and one is when scheduling options (F9).

 To change it at the project level click on the Projects directory on the left

then click on the setting tab 

then at the bottom under Define Critical Activities 

select total float less than or equal to 

and then on the right change the 0 to 10 or what ever your lowest float value is.

To change it in the scheduling option

select tools schedule

options (lower right)

then in the middle of the next page under where it says Define Critical Activities 

select Total Float less than or equal to 

and then under that change the 0 to 10 or what ever your lowest float value is.