Don't be concerned about the convention. The convention rate is usually for standard view, so those visitors often get the standard rooms. Swan/Dolphin give many upgrades, but nothing is guaranteed.
Join the Starwood Preferred Guest (SPG) program, which costs nothing. 1-877-STARWOOD
There are different ways of getting a higher status of SPG membership or special benefits (ie, AMEX GOLD,
AAA), so ask about this, if you have either of those. Some of the special benefits are late checkout to 4 PM (although we've been refused at the Swan once when they were busy --- they did offer to put us in one of their hospitality rooms) and guaranteed 1 category room upgrade.
Basic SPG membership gets you a special check-in line and the possibility of an upgrade --- we've gotten one X3, including during convention times. I've usually requested a balcony room ahead of time and also (politely and with a smile) ask if there's the possibility of a balcony room when we're checking in. The SPG program has changed so you're supposed to be able to use points to get an upgrade, if you call the resort a few days before arrival--- so I don't know if we'll get an upgrade any more without using points.
You earn points for every $$$ spent while at a Starwood property, and these points can be redeemed for upgrades, free nights, etc. Even if you don't think you'll ever stay at very many Starwood hotels, it comes in handy for check in and the possibility of an upgrade. There's also some type of 'instant reward' where you can cash in some of your points while at the hotel to eat dinner, etc.
Good luck!