I just restructured my rental property mortgage from 20 years to 25 years - we have never missed a payment either and have some savings (although not much). I declared everything on the statement, for the simple fact that they run a credit check on you as part of the process so I assume the savings will show up in the credit check (unless they are in the credit union - but I could be wrong about this!).
My bank (KBC) was very obliging about restructuring to make the repayments more manageable for us - even though we have never missed a payment so I don't think that would have much on of impact on their decision - however, with regards savings I am not sure whether this would impact your case, but again they run a credit check on you so I assume your savings would show up in anyway?