Problems with rapid melting ice cream. Making it without a machine
Most the time when ice cream is melting faster than it should, the problem is over-churning it. Like you said since that is eliminated due to the fact you don't have an ice cream machine. 

I would suggest a method I use: keep an old coffee tin laying around (one of the metal ones). Wash it out and dry. Then stick it in the freezer for 10-15 minutes or until it's cooled. Then make your batter directly in the can, then back to the freezer for a few hours. The coffee can helps insulate the batter and keep it cold even when it is out of the freezer. 

Then use the same food processor method as before. Scoop the ice cream mixture back into the coffee can and let it set in the freezer over night. The next day you will have perfectly scoopable ice cream that doesn't melt too fast.