A ductless heat pump may in fact be a great upgrade for you, given your current heating equipment. Other measures probably will be required as well to get a satisfactory outcome.
Some background first. A ductless heat pump has two parts. The first part is usually referred to as the outdoor unit, which uses an electric heat pump and some thermodynamic magic to extract heat from the air outside your house and concentrate it in a liquid 'refrigerant'. The second part(s) is usually referred to as the cassette or the head, which uses a fan and the hot refrigerant to produce warm air for your house. The cassette is a box about 6" tall and 3' wide which is mounted on an interior wall of the house and is connected to the outdoor unit with pipes and wires.
There are two potential downside areas to consider with a ductless heat pump.
The first downside is that heat is only delivered to the house at the location where the cassettes are located. This means that in most cases, a single cassette is insufficient to ensure that the whole house is comfortable. Multiple cassettes or other techniques are usually required to ensure that the whole house is properly conditioned, much like you now have multiple resistance heaters.
The second downside is that the heat pump does not circulate air well between different parts of the house. Air is drawn through the head, heated, and discharged back in to the same room. Of course, your current heating system suffers from this problem as well, but this can be more problematic as the number of heat source locations (cassettes) goes down from your current condition.
Together, these two potential downsides usually complicate a well-designed ductless-heat-pump-based heating system considerably, increasing the difficulty and cost of installation. The good news is that there are a variety of effective techniques for overcoming these problems, all of which will also improve the intrinsic energy efficiency and the air quality of your home. These techniques often involve reducing the air leakage and upgrading the insulation in the shell of your home, and installing some mechanical ventilation and circulation as well.
The specific design of the heating system and the associated shell and ventilation upgrades that will serve you best can only be determined during an analysis of your home by a qualified home performance contractor. Be sure to use someone who has experience with ventilation systems and shell upgrades, as well as experience installing ductless heat pumps in homes like yours!
Take the time to plan well and dedicate sufficient resources. Typically, we see about half the cost of a heat-pump-based heating system is the ductless unit itself, and half or more of the cost dedicated to other upgrades that are necessary to get the desired outcome. Ideally, you can expect to cut your electric heating bill by more than 50%, with improved comfort and air quality as well.
Vesta Home Performance Retrofitting