First "general" question, do you have to sleep on your back? I've laid down/napped in hammocks and am fine on my back, but I'm a side sleeper generally and I'm just wondering if that is a possible position.
Definitely not! Side sleeping in a hammock can be super comfortable, if you get the right hammock - that means either a wide one, so you can lay on the diagonal, or a bridge hammock, like the one sold by Jacks-R-Better. In fact, the bridge hammock lays so flat, you can even sleep on your stomach. There are very few other hammocks where that is true.
Now on to the specifics, I will be buying my first hammock at REI for the exact reason that you posted, so I am limited to their options. That being said, there is a huge price difference between the Hennessy and the ENO and Byer Hammocks. To your knowledge, is there a good reason why the Hennessy ones are so much more (my guess is name and the fact that they come w/ fly and bug net...but maybe you know more)?
You pretty much hit the nail on the head - the Byer hammocks are pretty much the cheapest way to get a hammock with a net, but they aren't as wide, and so it's tougher to get on a good diagonal for that flat lay that lets you sleep on your side. The ENO single isn't wide enough to lay on the diagonal, but the ENO double is plenty wide. However, by the time you add a rainfly and a bug net, you're pretty close to the cost of a Hennessey.
So it seems like the Hennessey would be the choice for you - HOWEVER, the tarp that comes with it is TINY. If you pitch it close to the hammock, you can stay pretty dry, but forget about hanging out under the tarp to stay dry while you cook your dinner. You very well might decide to add another larger tarp later, but that can be said about most hammocks. I have three different tarps I use with mine, depending on expected weather conditions and how much other weight I'm carrying.
Also, with the Hennessey, you enter from underneath the hammock - this is great for people who have trouble getting into a hammock, but a royal pain in the butt to get inside a sleeping bag when you get into hammock, and even more of a pain to get on top of a sleeping pad for insulation once you're inside. It will require some gymnastics.
Lastly, and maybe this is too much personal preference for you to be able to say, but of the Hennessys, I'm torn between the backpacker and the explorer. I'm 5'11," 165lb so the weight is no issue, but I'm wondering if I would really notice the difference in the added length of the explorer. Any help/insight you can offer will be greatly appreciated.
At 5'11, I would think the extra length would benefit you. Id personally try the cheaper one first, and if you feel cramped, return it for the larger one.
Oh yeah, I will be using this hammock backpacking in the summer time in the CO Rockies. In order of importance: comfort sleeping, bug protection (those kind of go together), weight saving, and of distant importance is site selection.
Any one of these hammocks will fulfill all of your qualifications. I would imagine nights get pretty cool in the Rockies, even during the summer - some people report getting chilled anywhere below 75 degrees if they don't have bottom insulation, so expect to need some sort of pad or blanket under you (not a sleeping bag, as the insulation will just compress).
Of the three, the byer mosquito has a bunch of ropes which can tangle, but it's also cheap and includes a bug net, and you can use any generic tarp you want. The ENO will provide tons of space, and has a bug net available for purchase, so it's very flexible, but not as nice of an integrated package. One cool feature of the ENO bugnet is that you can actually keep your pack inside the netting, keeping bugs out of your gear, which is kind of handy. The hennessey is the most complete package of the three, but you might end up wanting to replace the tarp anyways. The hennessey explorer is also pretty huge so should give lots of space, and is specifically designed for the kind of asymmetric lay you'd want given your desire to be able to sleep on your side.
In any case, if you do decide to buy a tarp, buy any generic camping tarp - NOT THE ENO DRYFLY. The ENO fly is a flying piece of crap - get a regular silnylon or polyurethane coated nylon camping tarp, and not that goofy ENO tarp.
Most of the small hammock manufacturers will let you try their hammocks for a month or so and return it if you aren't satisfied, but of course that adds the extra expense and hassle of dealing with shipping, which isn't as convenient of dropping by your local REI.