Where to start...
First of all, why are you trying to ride a goofy setup when you were doing well with your left leg forward? This is a very common trend among beginning snowboarders. I notice that a lot of times, a naturally regular rider thinks that goofy is more comfortable and vice versa. This is mainly because of the falling leaf thing that happens when you are learning. I used to think I was more comfortable riding with my right foot forward too. This is because every other second, I would start pointing downhill with my right foot forward.
Stick to your left foot forward since you were able to ride fine that way. You can leave your stance the way it is and eventually learn switch when you get better.
Secondly, you gave up way too quickly. Believe me when I say I hated snowboarding my first day out. I constantly fell and felt like trash the next day. I kept moving on though because quitting is not an option for me. The next few days were just as bad. But you know what? Once I was able to link my turns and stop properly, I was automatically hooked.
You need to take some time out to research stance angles and widths. This plays a huge role in how you snowboard. You need to play around with your stances to find one that best suits you. This might call for multiple trips to the rental shop between runs, but it will pay big dividends.
Lastly, you really need to consider purchasing your own setup. Rentals just won't cut it. Even if they rent out good boards and bindings, the boots will be an issue. Do yourself a favor and at least purchase your own boots. There are plenty of threads in this forums that will teach you everything you need to know about buying snowboard boots.
Don't give up! Going "too fast" is 99.9% fear. I used to think I was going to fast when I was learning, but compared to now, it wasn't even half the speed I go today. Learn how to stop and make wide turns to speed check yourself when you feel sketchy.
If money isn't a major concern of yours, you might do well by investing in some padded protection as well. This will literally save your ass many times over.