Well, I hope you are incredibly fast or have a great chin, because eventually someone is going to take advantage of your right being so low. If any arm should drop, it could be your left (orthodox stance), as you can still protect your chin with your shoulder, but dropping the right leaves you wide open and I don't care how big you are, a tap in the right spot is going to put you out.

About you squaring up as you get into it, I wouldn't say that is another stance, it is just a sloppy orthodox stance. If it feels better, fine, but you present much more of a target to your opponent. I also suspect you are not throwing your rights as effectively as you could. Standing square does not give you the ability to twist your torso and drive power from the ground up in delivering your punch. I can almost guarantee you are swinging a haymaker type of right in order to generate the added power you think you are getting.

My advice, practice presenting less of a target to your opponent at all times and keep your right up. Practice the weight transfer when throwing your right by twisting and pivoting on the ball of your rear foot. And, practice throwing out the jab. Eventually, it is going to feel a lot more natural - you will see even more power in both your arms (with the proper technique) and you won't be laying flat on the floor when your opponent manages to get in and tap you on the chin.

Salty is absolutely correct. If at all possible, and this goes for anyone, a boxing gym or trainer is going to make all the difference in your training. A site like How to Box is a starting point, but don't expect to teach yourself everything. I'm a big believer that you can do a lot on your own, especially conditioning wise, but to really excel you need that expertise and extra set of eyes watching your technique.

Not to mention that you miss out on the comraderie and social aspect that is involved in a good boxing club.

That said, make sure you keep visiting How to Box - I do throw down something decent once in a while. :)