Thanks everyone for the great feedback. At the very worst, I have confirmed that the beers in the first three years, that did not have quick staling issues, were not just good luck, and I have a great excuse to step up to kegging!
Below is a lengthy description of the beer transfer process, any constructive advice is greatly welcome!
As far as siphoning goes, in the post fermenting setup... that was the center of my attention this past few months. I started off using an Auto-siphon, (used this for three years of good beers, and then had 4 batches go south quickly with stale flavors). After having some issues, I purchased a new Auto-siphon, and had similar issues for two batches. So I tried new hoses for two more batches (using the new auto-siphon, and fresh pieces of hose for two batches.) When that did not work, I then purchased a stainless steel racking cane and ditched the Auto-siphon completely.
I also purchased some high-temp hosing, and started to boil that for 10 minutes prior to use with the Stainless racking cane. Using stainless, I can place a hose clamp around the hose and get a good seal on the cane... ensuring that the air bubble that often formed at the top of the cane part of the auto-siphon would not appear.
To prime the hose I first used the method of filling the hose with starsan water and starting the siphon that way. I found it a bit cumbersome, however, and I eventually found a turkey baster that I sanitized and used to start the siphon. (Kind of like sucking on the tube, but more sanitary)
As far as moving beer from primary to bottling bucket (no secondary).. I siphon to a bottling bucket, where I have boiled and still hot sugar/water solution. I then siphon the beer into the bucket, let it set for 10 minutes to a half hour while I finish getting the bottles ready
To bottle, I start the siphon and after the line if full of beer, I clamp the hose to stop the flow, but keep the line full of beer, and then I insert the bottle filler (non-spring tip type) and clamp that down too. I then run off 6 to 12 oz and begin bottling.
The bottles are Sam Adams or Bells bottles with crimp caps, all bottles are pop tops, and I have used a variety of caps, but not the O2 adsorbing ones. (I like to sterilize the caps, and some of the things I have read indicate that the caps lose their O2 adsorbing ability by doing this... but that is just here say)
So as near as I can tell, I am doing the right things on siphoning, and I do not slosh the beer around, so I am at a bit of a loss.
My thoughts presently are to possibly take the plunge and go kegging and buy a better bottle. Then I can push with CO2 at a very low pressure (plastic better bottle reducing the risk of exploding glass if I screw up) out of the bottle and in to a purged keg. At the very least that would isolate if the issue is with beer transfer methods, or if the issue lies elsewhere.
I have also been reading up on some fining agents, in the hopes of finding a lower cost fix. PVP appears to be the most promising, but while PVP claims to help reduce the tannins that are part of the staling equation, I suspect it will not cover up what must be a brewer/process issue.