I have not dealt with any of the Omega receivers, however I did have ADCO cut and thread the original 16" USC HK Barrel to 7" for $75 plus shipping. ADCO does fantastic work and it was about a one week turnaround.
I personally would stick to HK (best) or HDPS barrels.
Also, in my opinion a 7" barrel looks a lot better than the 7.87" barrels, despite 7.87" being the official length. 7.87" barrels don't look right without the HK mounting donut, and whatever muzzle device you install ends up sticking out much further with the longer barrel.
Just chiming in so you are aware of your options, and hopefully save you some hassle in the future.
Edit: Also my HDPS barrel would refuse to feed the top round of any fully loaded magazine, so I would have to "down load" to 24 rounds. With the USC barrel (that has the little ramp), fully loaded rounds feed no problem.