You should forget about Hardi Plank siding over the old stucco. The walls require a lot of prep work to properly install this type of product and can end up being very costly. If its not done right it will look wavey and if the hard coat stucco your home currently has will make the hard to do, thus the contractor may cut corners doing it.
The primary reason for the stucco failuer is water. I assume that the house has wood trim that over the years has begun to fail. Dry rot, not properly caulked etc. As water begins to enter around the window and door frames it begins to destroy the underlying base coat of the stucco finish. Thus the crumbling, powder etc.
I would not be concerned or wait for the guy 50 miles away. He most likely will not do the job or price it so high that it would not be feasable to do it. Costs of fuel, and size of job is the factor here.
So what to do. I would consider the EIFS option. Unless your willing to pay to have the hard coat removed. This is a very costly and time consuming job. You can expect interior damage to the walls to be uncovered that you, once uncovered will have to deal with.
EIFS also will be a little tricky. They will have to remove the damaged areas and replace with new plywood to bring the surface back to level. Once done they then can install the EPM board (styrofoam) back onto the walls. Then Rasp level and complete the job. Once done it then can be re-base coated with proper mesh and then finished coated to the desired finish. It is very inportant however that the details on the installation be followed down to the last part of the job. Not doing so will cost you over time with water intrusion and additional hidden damage.
The reason I suggest using EIFS over the hard coat stucco finish is that it will benifit the house in many ways, The EPM board will provide additional insulation to the house which I am sure because of its age it could use. The EPM board acts as a buffer to the finish coat. Traditional stucco homes tend to move, thus the stucco cracks. The EPM board allows for this movement without the damage to the surface of the lamina.
But once again the details around the openings are the important thing. Proper backwrapping, caulking, before the finsih coat goes on, flashings above windows and doors. Proper sealant around lights etc are all critical to prevent problems in the future. Also the EIFS cannot be set into the ground. It must teminate at least 8 inches above grade, four inches above any roof shingle. and at least two inches above any porch deck.
The EIFS contractor most likely will tell you that he or she has been doing this for many years and they understand how to do this properly. I can tell you I have been inspecting this stuff for the past 14 years. And only have seen it done right a handfull of times. The average homeowner and builder does not understand how this is supposed to look and be installed. Right down to the new drainage systems. Which in my opinion are harder to install properly then the ones that were considered barrier types. Thus because they could not do the basic systems right, do you think they will get the more difficult drainage systems on corret?
Contact the Exterior Design Institute at
http://www.exterior-design-inst.com/ once your there click on find an inspector. They can assist you in getting the job done right. Also they can evaluate your homes current stucco system and help determine why it failed and how to do it properly.