There are a few common approaches you could take to fixing this problem.
#1- make your Omega work. This involves learning new techniques or tuning your existing techniques. Either way this probably isn't going to be a short process but your game will benefit more from this approach... eventually.
#2- beat your Omega until it is less overstable. This will take a while. You can fake it by throwing it into a brick wall, tree, asphalt, etc. but it will not fly as well as a disc that is naturally beat because of a hundred rounds worth of putting and approaching. This option might take even longer than #1 but you might be well on your way to having a beat Omega if you choose to go with option #1. Don't forget to add another new Omega so you can have an overstable compliment to your "new" beat Omega that is less overstable.
#3- buy another Omega in a lighter weight. Lighter discs will go further with the same effort (at least in the 60' to 150' distances we are discussing). Your putting range and approach range should increase a little by going lighter. But wind will also affect your putter a little more if you go lighter and you will have to re-learn your drop rates because the lighter Omega will carry a little better.
#4- try a different disc. You complained about how deep the Omega. Options #1, #2 and #3 above won't fix that. Your Omega has a 1.5cm depth. Putters that are shallower than the Omega:
1.1cm depth
Aerobie Arrow- not a traditional style putter; it has odd flights IMO
DGA Blunt "Blowfly"- can be really floppy; a few people really love this disc but most golfers just don't "get it."
Innova Aviar XD- solid choice. It is a modified Aviar... XD stands for extra distance
1.2cm depth
Discraft Ringer- never thrown it
Innova Classic Roc- in between a putter and a midrange; not a bad choice
Vibram Summit- never thrown it but from what I understand it might be a solid choice for you
1.3cm depth
Discraft Zone- probably too overstable for what you want
Innova Aero- solid choice
Innova Rhyno- great disc but not what you ar elooking for 'cuz it will be too overstable
Latitude 64 Spike- probably too overstable; never thrown one.
1.4cm depth
DGA Reef- same mold as Discraft APX
Discraft APX- the disc I would recommend for you; solid choice
Discraft Magnet- another great option but it feels deeper than the numbers suggest
Innova Dart- great choice
Innova Hydra- probably too beefy for your requirements
Innova Mako- another putter/mid but biased more towards midrange; good disc but might not be the best choice unless you get a lighter weight.
Innova Pig- toooooo overstable
Latitude 64 Pure- another candidate in the "solid choice" category
Latitude 64 Sinus AP- flies similar to your Omega
Latitude 64 Sinus SP- flies similar to your Omega
Quest AT Crossfire- never thrown it
Wham-O 86 Mold- never thrown it but I understand it to be a finessey kind of putter
After looking at the discs that are shallower than the Omega I would have to say the APX/Reef is my recommendation for the shot you want. The Gateway Magic is similar to the APX. The Magic is the same depth as the Omega but feels shallower to me because it does not have a bead. So if you are keen on trying out some new plastic then I would add the Magic to the APX/Reef recommendations. The P&A Aviar is also a good disc that doesn't feel as deep even though it is listed as being the same depth.
There are pros and cons to any of the 4 options I outlined. Choosing the right option for you involves recognizing your priorities and matching those to one of the options above.
If you are getting serious about disc golf and you are competing in/thinking about competing in tournaments then I would strongly suggest option #1.
Feel free to ask for more info.
