If you keep it indoors then yes it will be floppy and etiolated.Aloes need strong light to have stiffer leaves and shorter internodes.Even your careful watering isnt a solution (and from my experience common cactus mix soil stays wet too long)to your problem.

Also, the soil needs to be cut with something like 50% perlite to make it more porous (aloes don't like heavy soils).
There's more in the link.

Here is a link that might be useful: Aloe FAQ