I would say the answer here depends on your true focus. From what I'm understanding, you have two goals:
1. Learn mixing, learning mixing in Sonar, sort out the best monitoring option using what you have available.
2. Submit this particular song to a competition.
Honestly, if #2 is the most important goal right now - and you have the limitations of inaccurate monitoring tools and are new to mixing - I'd bounce the tracks and have someone else mix. Then send out for pro mastering. This isn't to doubt your ability to learn mixing, just trying to be practical. I've mixed for many years now, and if I ran into the monitoring situation you have while entering a song competition, I would find someone else to mix.
That said, if the competition is secondary, or you really are determined to mix for the competition, I would probably use the the hi-fi system to mix. There are inherent issues with this! This system sounds too good, probably deals with lower frequencies much better than the average listener's stereo, and does other processing that will make a mix sound better. As Sanderxpander said, I'd listen to a ton of similar music through those speakers to get your ears tuned to them, and then reference back to those songs frequently while you're mixing. Then I'd use your headphones as a comparison. They won't support the same frequencies, but you'll most likely hear if horrible mids or highs are too dominant in the mix. Work slow, compare, make small adjustments, repeat. If you can use your car stereo, it's usually a great reference as well because lows and low-mids will generally punch hard and sound pretty bad if they're too boomy. Plus - you've probably listened to a lot of music in that stereo and will be most familiar for comparison.
For mastering - again my first recommendation since you have the competition is to have someone else master it. Ideally, find someone who will master from stems instead of a stereo track so they have a little extra control to help correct anything really weird in the mix. I should stress that mastering shouldn't generally be used for mix correction, but nonetheless. Find someone who will be cool about it, and let them help you by giving them stems and make some adjustments.
If you really want to do it yourself, here are my recommendations.
- Get your mix as close to the right sound as possible before mastering. Don't rely on mastering to finish your mix.
- Because of the monitoring limitations, I'd be careful applying presets that give a large color change to the song. In Ozone, "Mix master" seems to generally work well for some leveling things off and level boost without crazy color. The 4 band presets toward the top of the list can be okay too, but add more color.
- Due to the monitoring limitations, I'd recommend not pushing the mix too loud. It'll be nearly impossible to get a commercial volume track with bad monitoring without squashing the song. I'd just accept it will be quieter, people will need to turn it up a little, but you'll have a better sound overall.
I hope that helps!