Selvedge Theories

While waiting for my yarn-jello to dry* I decided to do some research on the trust Inter-web to see if I could figure out why I have been having problems with floating selvedges on my twill weave.  I firmly believe there must be a Rule, and it must one that can be simply stated.  Seriously, it's a 4-shaft pattern, the variables are the directions from which I throw the shuttle, where in the treadle pattern I start, and which direction I decide the treadle.  How many ways to screw this up are there? (no comments from the math people)

I have found the following two possible Statements of the Rule which I will have to test out. First, from Gilmarka's Weaving FAQ:

"If you are weaving twill and that uncaught selvage thread is part of the design and must be caught, start the shuttle on a different treadle or from the other side. It will usually catch if you start in a different place in the weave. If the first and last threads of the warp are on odd and even shafts, the weft will catch all the selvage threads as needed, but you need to start with the first weft over the threads on the even shafts..."

I'm not sure what they mean but "start with the weft over the threads on the even shafts" since when you weave twill the tie up is always going to have one even and one odd shaft, so 1-2, 2-3, 3-4, 4-1.  Maybe you have to start on 2-3?  This makes sense, but also does not take into account the direction from which I am throwing my shuttle.  Unless it makes no difference.

Second, we have the Alaskan Fiber Arts tips page:

"In weaving a Twill, 2/2 or whatever, on a 4 harness loom, use:

• Thread left side on an even shaft, 2 or 4.
• Thread right side on an odd shaft, 1 or 3.

This catches the selvedges on both sides. This is the way it's threaded even if it's out of the pattern sequence. No floaters to fuss with, no wasted thread. For a 8 harness loom, use:

• Left side ends on an even numbered shaft. (2, 4, 6, 8)
• Right side ends on an odd numbered shaft (1, 3, 5, 7)

So let's do a little 2/2 twill threading on a four shaft loom here:

1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4

Ok, this is the way it would be if threaded straight across, yes? You're looking at the loom from the front, the 1 is on the left, the 4 is on the right. But this should leave a dropped (not caught) warp thread, most likely the 1 on the left. (Assuming you start throwing the shuttle from the right.)
So to fix it so that doesn't happen, thread like this:

4, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 1

The main thing about it is to have that last warp thread out of sequence."

Thinking about this, I *think* it's just possible they are saying the same thing, more or less.  It seems like the Alaskan approach might work better if you are doing a diamond twill or herringbone or some other pattern that changes directions.  I know it's possible to do a straight 1,2,3,4,1,2,3,4 threading and get a perfectly neat selvedge with no floats, as I have done it, I just can't figure out how to state the rule for when this will happen and when it won't.

*No, I did not use jello, I used gelatin, it just sounds better to say yarn-jello.  Besides, the left over sizing smelled and looked an awful like like sheep flavored jello once it set up