Measure Using Relationships to create Matrix

I have worked on a similar problem. This may or may not be an optimal solution, but I think it will work. 

1. First create relationships between the following:
   1. Main Table & Cost Element Table on the Cost Element
   2. Main Table & Employee Lookup Table on the Employee # 
2. Second Create lookup columns (I'd do this with DAX) on the Main Table to get the following: 
   1. Account from Cost Element Table
   2. Budget Group from Employee Table
3. Third, create a concatenate of the Account and Budget Group on the Main Table. (You could consolidate steps 2.1, 2.2 and 3 into a single step with the right DAX)
4. Fourth create a concatenate of the Account and Budget Group in the Budget Table. 
5. Fifth create the relationship between the Main Table and Budget Table using those concatenated columns. 

If I understand your dataset correctly this should give you a 1 to many from the Budget Table to Main Table (respectively). If you need help specifically with the DAX just let me know. I didn't include it to save time in case you already know how to write those.