I understand that it would be difficult to dig holes for a concrete footing for your posts. Depending where you are located and the soil types, you could drive the posts in and still have a stable fence. If you are in an area with frost in the ground, I would encourage you to set them at least 3 feet deep if the soil is stable and compacted. The basic rule of thumb is to bury at least a third of the posts, but half the length is even better if you can do it.
I have only done this once, in my own backyard, but I am also in the business of aesthetics, so I thought I would chime in. In my situation we went with option #2.
I would not recommend option #3, due to purely aesthetic reasons, unless you would like to keep the fence low all the way down for some reason (light, neighbors wishes, view). Having the gate suddenly jump up by 4' at the end would be quite strange looking, in my opinion.
If you go with option #2 the fence will be high in the back corner, which will allow for taller plants and more landscaping options, and will just look better in general. You get the same effect with option #1, however, it is more of a pain to do all the cuts necessary to slope the bottom, which after a little bit of growth from the landscaping you will never see. It would really be a pointless detail. In my experience, once we got building we were very happy that we had decided against doing that very thing- it's enough work already! And after just a couple months of growth the bottom of the fence was totally obscured anyway.
I wonder if your house is a mid century style? Horizontal fences always look great with this style of house- I also prefer them over vertical for almost everything. I wish I could send you a pic, but I don't live in the house anymore and am renting it out. Anyway, I hope my two cents helps you decide!
Best Answer
I would need to know more about the existing condition of your fence. If you could send me a picture that would be great. I would definitely recommend that your existing fence be in very good shape if you were going to add on to it. If it were old and rickety it wouldn't do you a whole lot of good to put new materials on top of it that's for sure. There's a lot of things to consider. Are you a fasteners I.e. your nails or screws coming loose on your fence? Is the wood rotted or warped? All that stuff makes a big difference in what you are asking. Another thing that is very important is your 4x4 post that are in the ground if they are loose I certainly would not add more weight to the fence. I would hope they were set in concrete from the beginning If they weren't I wouldn't even consider doing this.