You aren't moving far enough away.
When you create a nether portal, the game searches in a radius of 128 blocks in the dimension you are traveling to, for an active portal. Since 1 block in the nether corresponds to 8 blocks in the overworld, you will actually need to travel at least 1024 blocks from your original portal in the overworld in order for the game to create a new portal.
Once you have done this successfully without falling into lava, you can make your way to the original portal and destroy it. Then you can create your portal in the nether wherever is most convenient for you, nearby the original one, and your first overworld portals should connect to it when you light it up.
It is surprising that you have nowhere to stand on your portal - I was under the impression that if a portal was created in the air, there would be an extra obsidian platform around it so that you didn't immediately fall off. In fact, if you just don't move when you first enter the portal, it shouldn't make you fall, you should be standing inside the portal. You can then hold shift to move slowly and avoid falling off the edge (holding shift prevents you falling off a block) and build away from the portal till you reach solid ground. If you do in fact fall immediately upon entering the nether, that's a glitch that I've never heard of.
Note: It is still possible to have multiple portals in a small space that all work properly and connect to the right portal. The key is that the game looks for the closest portal in the destination dimension, so if you build both portals in the "right" places (overworld x and z divided by 8 in the nether), before lighting either of them (Obviously you need an original set of portals to do this), then you can connect them properly.