I have never been able to get my San Juan 34 to stay put with a single anchor setting. It will sail all over the place and, if the winds are strong enough, will eventually wrap the chain around the set and drag. I always set out bow and stern anchors at night or if I leave the boat.
The problem is that in very crowded anchorages I am always on the look-out for swinging boats. That usually leaves us in the outer reaches where it is very bumpy or crammed into some pretty tiny holes with little room for cushion in case of emergency.
Anybody have any suggestions?
If you are needing to set two anchors for routine anchoring, you definitely have a problem that needs fixing. Plus, you are not going to make any friends by dropping a stern anchor in an anchorage where everyone else is swinging on one anchor -- that's a fairly serious breach of anchoring etiquette. And, while you seem to be minimizing the effect on your neighbors by heading out to the periphery of the anchorage, doing so is a pretty big inconvenience and hassle for you, I'm sure. So we need to find a solution for you.
The riding sail suggestion is a good one. We've used them in the past with great results.
You didn't mention whether you have a roller-furling headsail, but these can be another big factor in how much a boat swings at anchor. Some boats just don't do well with all that windage forward. The riding sail can help counter that windage, as would making sure you get a VERY TIGHT furl to reduce windage. But with some boats, the best bet is to drop the roller furled headsail while at anchor in any amount of wind.
I also would agree that your choice of anchor/rode combination is less than ideal and probably contributes to the overall problem. The typical-sized danforth-style anchors are fine as supplementary anchors, but do not usually make the best bowers. You might consider a beefier arrangement and adding more chain to your rode.