Ok, this is fairly complex and the beginning of my research. I'll do my best to present it.
Nah, not complex in the slightest.
I have 4 Bose 301's, I've come to the conclusion that my intent of tacking on a center speaker and a woofer would be insufficient and woefully inadequate compared to the other 4 bose speakers,
I don't think adding a center channel would hurt you, as long as it can keep up with the higher efficiency of the Bose 301s. Do you happen to know what generation they are? It should have a roman numeral designation on the back of the speaker. I know these speakers have a bit of a cult following and are basically the second most highly regarded of the Bose speakers (second only to the 901). All that said, at the very least you would definitely benefit from a subwoofer.
and after some thought and some brief experience, I realize that despite surround sound, most of the important sounds come out the center speaker. I want to utilize my 301s. Further, even with regular Dolby 4 speaker surround its still pretty damn good.
What is the make and model of your current receiver? You are correct about the significance of the center speaker, however it's not entirely a poor setup to run a phantom center. This just means the sound that would normally be played from the center channel is mixed into your front left and right channels in a surround sound setup.
1. What I want: A stereo receiver with optical audio or HDMI and 400-600 watts of power to fuel the 4 Bose 301s. If this kind of receiver is out there then my search is over.
1. You don't need want a stereo receiver if surround sound is your goal.
2. Your speakers don't need that much power. 50-100 watts per channel is all you will need for those, they're fairly efficient IIRC.
2. I want full use of my 4 Bose 301s with out missing audio.
Then you definitely want a surround sound receiver. Most if not all modern receivers can be configured to run in phantom mode so all the sound from the center is mixed into the left and right channels, so no loss of audio information, though definition won't be as good as it potentially can be with a proper center channel.
3. If only 5.1 receivers have a digital in, and I go with one, but only have 4 Bose 301's to hook up,
a) can I still get full Dolby surround sound or am I doomed to always miss the dedicated sound coming out of the center speaker and woofer?
Nope, no rule that says all the channels of the receiver must be used in order to get all of the "sound". Again, this is where "phantom center" comes into play.
b) will setting my Xbox One to plain Dolby stereo Surround AND digital audio out (optical wire or HDMI) still give me full sound or will I be missing a center and woofer sound as in mentioned in "a".
If you set the XBOX ONE to stereo only it will downmix multichannel surround into 2 channel stereo, or 2.0. This means that all the multichannel information will be mixed into just 2 channels. Then again, this depends on the media in question. Sometimes the media will have a separate premixed 2 channel track that will be used instead of using a downmix, but the result is essentially the same. If you're going to be using a surround sound receiver I would recommend leaving the XBOX ONE set to multichannel and let the receiver handle any downmixing itself if necessary. If you limit the output to Dolby Stereo surround the receiver will only receive 2 channels. The only way to apply surround sound to 2 channel is to use a matrixed surround like Dolby Pro Logic or DTS:NEO which is a post process, not as good as true dedicated multichannel. By leaving the XBOX ONE set to multichannel a surround sound receiver will receive the whole original signal. If you're still only using the 4 Bose speakers you'll at least be able to have a 4 channel signal instead of 2 channel.
c) basically what I want is Dolby Stereo surround through a digital cable. Will a 5.1 receiver allow this or will I be doomed to missing out on a center speaker and woofer, or will I be doomed to a red and white cable?
I think if you read the above this question becomes null. You're not forced into losing the audio information that the center speaker would have played. In the receiver's settings by simply setting "center speaker" to NONE it puts the receiver into phantom mode which as mentioned before mixes the audio information that would have originally been played through the center speaker into front left & right speakers equally. No information is lost.
