As petermac87 responded, check the thread he provided and you will see plenty of info. If Apple will assist you, of course that is your best bet.
Now, to answer your question directly, yes, there are options. Here is the one I used. Remember that the spring tension to hold the iMac screen in position is provided by two springs. The inboard tang on each spring is held in place by a plastic washer, as seen in the aforementioned thread. If just one of these washers breaks under the spring's tension, you will no longer be able to adjust your screen. In order to PERMANENTLY fix this, replace those cheap plastic washers. There are sites on the web that will show you how to disassemble your iMac to get at the hinge. Be warned, you will COMPLETELY disassemble your iMac and it is not a task to be undertaken by someone with little patience. However, if you are fairly competent with hand tools, the job is fairly straightforward. (This is also a great time to upgrade your hard drive as I did, replacing the stock 1TB unit with a Seagate 3TB. Make sure the replacement is compatible.) Once the iMac is disassembled (all parts including logic board), remove the 9 torx screws holding the stand to the hinge and remove the stand from the hinge. Next, remove 6 torx screws holding the hinge to the iMac rear case. Now, remove the two torx screws in the center of the hinge...CAUTION! if any of the plastic washers are NOT broken, removing the screw holding it will cause a sudden release of spring tension! I recommend doing this with a towel covering your work as you release, or using a pair of needle nose pliers to hold the plastic washer and its underlying spring tang in place. Now, use two #12 stainless steel flat washers, or equivalent, in place of the plastic ones. Two things to consider when choosing washers:
1) The inside diameter must be large enough to go around the post that holds the screw
2) The outside diameter must be large enough to cover the spring tang, but small enough to not interfere with the spring itself.
Use a pair of needle nose pliers to hold the inboard spring tang down to the hinge plate. While you have this done, place one of the metal washers over the shank of the screw and install the screw as far as you can by hand into the hinge. This will be enough to hold the spring tension as you remove the needle nose pliers. Now, use the pliers to center the washer. This can be a little difficult as the spring is putting tension on the washer. Once you have everything just right, tighten the screw all the way down. Replace both sides, even if only one was broken. Put everything back together in reverse of the way you took it apart.
This repair cost me $19 for new screen seals, and $2 for a box of #12 washers. Time investment was about three hours. I am back up and running now, better than new! Good luck!