I've not tried the Omega, but looking at the auger, I am very doubtful it would work. It's a very powerful press, but has no cutting ability, which cocoa needs. As a juicer, it works great, but cocoa isn't juice or a fruit. Also, one of it's selling points is that it runs at 80 rpm - and is cool. Exactly what you can't have for chocolate as it needs friction to liquefy. The Champion juicer works because the teeth on the cutter wheel chew up the cocoa, releasing cocoa butter trapped in the cells, allowing the whole mixture to flow. And it generates a good bit of friction partly by running at 1200 rpm.
The rule of thumb I have learned to use for evaluating different juicers and grinders for this case is asking 'will it make nut butters?'. If the answer is yes, it will work for chocolate. If no, it won't. I've yet to have this evaluation not work. As for the Vita-Prep 3, I know it will not work. I tried it early on. It burns the chocolate by running too fast. In this case it's is too much power and friction and the fact that the chocolate has nowhere to go once it starts to liquify.
This final part (a place to go) is why (in my opinion) the Champion works so well. It cuts open the cells. It creates just enough friction to melt the cocoa butter. And once the butter/liqueur is flowing, it is removed from the area by coming out the screen or snout so it does not burn.