This type of repair is typical to owning a historic / older home. The longer you live there the more times this same dilemma will appear. Normally folks who buy such houses spend the money as a labor of love. If you bought this house as a money making investment, it probably was not a great idea. It was low priced and the bank dumped the property for a reason.

Most older homes were built with undersized lumber for today's standards for deflection. The re-framing for stiffness, tiling and sagging is normal. Sistering should be full span only and every joist.