csscott -
Any OTC unit is going to have more people than you're probably used to on those deer and antelope hunts. With that being said, opening week and weekends tend to be littered with people but by Tuesday almost any unit in the state calms down. Unit bundle 44 has a lot of public land and is a good overall unit for OTC, but hunters are around.
I'll also say, if you think you've packed in far enough, you haven't. It doesn't matter how far you go, there will be other hunters, hikers and the stray dog at times...

ok that's little exaggerated but overall Colorado is known to have great trails in our mountains and public lands which once again attracts people. Remember if you go in, you've got to be able to get the animal out. 12 miles sounds great, but the reality is not too many people can get an elk out on their back being in 12 miles...
Not trying to sound like Debbie downer, but strategic planning works better than the "farther, deeper, off the beaten path" approach. I've hunted CO for nearly 20 years (15 as a nonres) and there are some great units (OTC) that can provide you a great experience.
Lastly, look at units that have more tags, yes that means more hunters but it also means more elk!!! You can make other hunters work to your advantage too.
That's my two cents.