You could consider an FHA 203K Rehab loan. This is a single loan that refinances your existing mortgage and provides additional funds for the repairs/improvements. It is based on the after-improved value. However, one key caveat – you cannot perform the work yourself, it must be done by contractor(s).
An FHA 203K is an option to make improvements to your home, but it would not be my first choice. The 203K is expensive and requires extensive documentation.
You should be able to get a home improvement loan that is based on the improved value of your home. In addition to an appraisal for the ‘as improved’ value you need a contract with a general contractor that includes the cost of the improvements and includes plans and specs for the work to be performed. The contract should establish a material and mechanics lien on the property. The draw(s) from the home improvement loan will satisfy the mechanics lien. The lender may require that the first draw pay off your current lien to give the lender a first lien position. These procedures can vary from state to state; and lender to lender.
It may be possible to refinance the home improvement loan into a conforming conventional loan after the improvements are made.
I don’t understand why your bank would refer you to a finance company. Contact a few community banks until you find one that does home improvement lending in your area.