Congrats! and great job improoving your scores.
This is a good lesson about the abysmal state of credit knowledge some mortgage brokers have.
All I know (now) is that FICO is what's important when applying for a mortgage. The other scores don't matter. Just keep plugging away and GW your lates and dispute the errors. It'll get there. You just need the middle score of the three FICOs to be like a 620-640 for conventional and 580 for FHA. Let me know if I can help in any way. Good luck!! 
For mortgages FICO is what determines your interest rate, especially for conforming loans, but you still have to provide tax returns, income, and expense or bank records for the initial underwriting. The reason is that conforming loans are typically guaranteed and securitized. Once the loan is done your FICO is tracked together with that of other loans in the portfolio and they no longer have access to your other details. FICO scores are how they value the portfolio over time.
There is a huge amount of historical value agencies have relative to FICO scores so it is extremely difficult, bordering on impossible, to use other scores. This is the main reason Fair Isaac is so dominant and it's unlikely to change.