You have several issues that make your project a fun one. The age of the building will require that you work with design professionals and contractors who are familiar with historic renovations/restorations. Even though your house may not be a historic building, the construction methods and materials are similar. As an example, it will probably prove easiest to build a floor hatch to get to your crawlspace; you want to ensure its location and construction are such that do not detract from the home or add other maintenance issues later.
You also are dealing with a structure that has proven the test of time. A crawl space that is 100+ years old should be extremely dry. This makes the dirt in the area turn to a fine powder; so anyone who does access this area will need to take special care with mouth & nose protection and coveralls. Because the house has stood so long, and the problem is new, you need a building analysis to see what has changed.
What have you done or had done in the past year? Something as simple as paving your driveway may have an affect on the way water was leaving your building. A new roof or gutter may have water draining the wrong way, and it is getting under your house. New insulation added? Landscaping around the house may be to blame, etc.
For the crawl space to be the cause of musty smells and rotting floor boards, moisture must be present. Is it possible the chimney has begun to leak and allowed water to get all the way down to the crawl space? Is it possible a plumbing leak is allowing moisture into the area? Has the outside landscaping or terrain been changed, where the ground water, rain water, etc would have changed? Where are the floor boards soft; what is under them or over them that would encourage rot in these areas. (Near a heat vent? Under a window? Middle of the room?)
Have you changed the air conditioning unit or installed central air recently? Older homes take time (sometimes years) to get used to artificial conditioning. So an older home that had window unit AC and radiator heat, will take a few seasons before the humidity and moisture in the building materials balance back out from central air or forced heat. If the house sat empty for any length of time would cause this to happen again.
As you can see there are a lot of fun options that should be explored to ensure the exact problem is pinpointed. I recommend, almost always, working with a licensed Architect. There are firms that specialize in older structures and facility management, where they will be able to investigate what has caused the house to have these issues. (My firm does this service, and it is a lot of fun to investigate these older buildings; they are masterpieces!) They also will be able to recommend strategies to correct the issue to allow for budgeting options. And they will be able to recommend any specialists or contractors who would be able to perform the work.
Another option, that is just for fun, is you could under-pin your building. This is the process of putting in walls in the crawlspace in a methodical pattern until your entire house has walls under it instead of the foundation. Then they remove the crawlspace dirt and you have a basement. This is often done on older homes to increase the square footage, reinforce the foundation (if needed) and allows for the mechanical systems that didn't exist when the house was built to be located out of the way. Your archtiect will be able to find a structural engineer to help with this process, too!