Conclusive Fragmentation Evidence Required

Currently managing a VLDB which is heavily fragmented. The applications characteristics are heavy INSERTS, UPDATES and DELETES and against my recommendations the majority of the large tables are HEAPS or have inadequate non-clustered indexes. The code is dynamic SQL, the tables dynamic and the vendor's understanding of SQL is poor which hampers my progress here.

Both the OS defrag GUI and sys.dm_db_index_physical_stats show huge amounts of fragmentation, some tables are around 80%. Note: (Indexreorg jobs are in place where indexes are present)

The problem I have is convincing the windows engineers whom contol the budget that deploying a defrag tool such as Idera's Defrag Manager will actually be of any use. They keep asking whether the app will actually will get inside the DB and I'm curious whether there will be any benefit on the HEAP tables should the vendor not make changes to their code.

Is there any conclusive evidence I can provide these Window guys to quantify my defrag expenditure request? Any help would be appreciated