I'm still very much in the learning process of taking great full frame photos of birds myself but can pass on some things that help me get very close to birds in Northern Mo. As stated before, some birds will allow your close proximity more readily than others and the more they become accustomed to you the easier it should become.
Some things to try until you buy a longer lens, keep all movement very slow, wear dark or drab colors, try to break up your outline, if you have a large tree try sitting with your back against it facing the birds. For me a blind is very helpful for the most wary birds, for economy and to see if you want to continue, try using an appliance box obtained free from a local appliance store. You can cut shooting holes anywhere you like, modify it in any way, throw it away and start over at anytime. The box blind will soon let you know if you might want to purchase a camo pop up blind in the future.The blinds are also helpful for me to shield from the cold winds we have in winter here, in your case the hot Florida sunshine.
Most of my birds, especially those low in pecking order will fly in, grab a sunflower seed and go to a close perch to open it, so a couple of perches 10 feet or so from the feeder may be where you get the best shots anyway and can give a more realistic shot that the pros on here are always getting.
My most difficult small bird has been the Tufted Titmouse, they never sit still and do not stay at a feeder, they grab a seed and go to a nearby perch to be alone.
At my place some birds come in early and late in the day but seldom while there is real good light, others may show at anytime and all day long,so one has to stay as prepared to shoot as you can be.
WARNING! When I bought my DSLR, it was for documenting places I travel and family photos, wasn't overly concerned about great quality. Saw the pics on here in the Wildlife and Bird section, was so impressed when viewing them and learned a great deal from helpful people that I started "practicing" on my birds. Soon found myself buying the 150-500, a monopod, tripod and I have a very long ongoing wish list, all of which seems to be very expensive. Hope you enjoy shooting birds as much as I have and please share your experience.
BTW, for me the black sunflower seed is the best all around seed I've used so you should be well on your way to having several dependents showing up in your yard soon.