Having lived in Ecuador for almost all my life i can give some information.
You say you have a remote tour, that sounds like you are not going to be near mayor populated areas in Ecuador, so if you're going to the amazon jungle, forget about taking your Harley Davidson with you. Instead you can buy a cheap dirt bike and enjoy.
If that is not the case and you are going to be near a major city, go ahead and take the sportster.
I have not ridden through Central America but i know it is an adventure on its own, if you decide to fly the bike, you could have some problems with ecuadorian customs, depending on too many variables, like the city your bike arrives, they day of the week you try to get the bike, your level of spanish, you attitude with bureaucracy, this is important because if you get frustrated and show it, things will surely get real bad, i don't think you can get a temporary import permit for a full year, try to include your bike in your belongings with your military unit.
You can find many cheap secure places to store your bike on any medium or major city, the riding is great in the mountains and in the coast but washed out parts of roads are very common and very bad sections can be long, it is not fun on a cruiser, been there done that.
I don't think you are going to have problems with military bases if you have the proper identification and permits for you, not the bike.
You can ride all year long in all parts of the country, you just have to adapt to the weather, from Dec. to May it rains a lot and it is very hot in the coast, in the highlands it can be very cold, wet and sometimes you can see hail.
If your bike is not FI, you have to adjust the air/fuel mixture for better riding at altitude, it is common to be at sea level in the morning and at 13000+ feet altitude for lunch.
Insurance on the bike can be expensive, HD bikes are double the price in Ecuador and theft is not rare, but if you wear military gear thieves will leave you alone, specially if they can see your gun.
If you don't want to risk you life in deadly traffic avoid riding in Quito or Guayaquil, most people don't obey traffic laws, it is organized chaos, but if you enjoy adrenaline and can control yourself you'll like it.
Hope this helps