I am not clear on your exact problem. Perhaps you could be a little more clearer.
If you are designing a garage "new", you should have fewer problems as you described. I assume that you are trying to tie the elevation of the floor you are putting over the garage with an existing floor (perhaps) in your house. Since you want to clear span, you have decided to use the 14 inch J series joists. That is good. But why for the price of a few more dollars don't you "finish" the project now. You are saving very little if any by not installing the remaining floor that you want while you are at it the "first" time.
Anyway, instead of using the 14 inch joists, you should probably concider using nominal lumber. "How in tarnation can I use nominal lumber and clear span my garage" you ask? By breaking down the spans into workable sections. I would recommend that you istall steel "I beams" centered each side your garage doors. They easily span the 20' and you can run your joists perpendicular to the beams. If you figure you have a 30' garage, that is three bays and only 10' spans. Piece of cake, my man. You can also figure out your mechanical delivery. Instead of making materials do something they don't want, reconsider your materials and methods.
Steel beams are cheap. And not only can you size them to carry your floor load, you can, for very little money, size the beams to carry your "roof" load. You can, as amazing as it seems, put columns centered over the beams and hold up your roof framing, since you wish to occupy the area and normal trusses are out of the question. This is easier and cheaper than scissor trusses or some other method of framing. Only problem is, you will have two columns upstairs in that floor area. Think it thru. You may need to discuss things with a structural engineer (always a good idea anyway) before you start hammering and nailing and buying materials.