Without access to FEM program, you have to refresh or learn the "Column Analogy Method" developed by Prof. Hardy Cross. Here is a paper provides the basic for using such method to find the fixed end moment, carry over factor and distribution factor, that all are required for solving indeterminate beams with the varying moment of inertia using the moment distribution method.
Albeit this paper was written for the author's computer program, nevertheless it is a good start point. PRINCIPLES OF THE COLUMN ANALOGY METHOD
Also, please keep in mind, depends on the depth-span ratio, the beam might be classified as a deep member, given your situation, it would be very difficult to get results with high accuracy without using FEM or classic advanced analytical method. You can try to use the "truss analogy" that is considered more appropriate for problems involving deep members.