The definitive source for Sous Vide information on the web at the moment is Douglas Baldwin's wonderful A Practical Guide to Sous Vide. It has wonderful safety information and goes well beyond the 'recipe' side of Sous Vide. It's pretty much the bible (since Modernist Cuisine is too expensive).

Based on the information he has on pasteurizing eggs, I would suggest trying a shorter period of time. He says that 75 minutes at 135F will be sufficient. If you read through his stuff, you'll see that he doesn't play fast and loose with safety / times, so I would trust that time / temp. That's significantly shorter period than you are doing them. Hopefully that's your issue.

I'm not sure how much your white is coagulating, but this is what he has to say about it:

While the properties of the egg yolk are unaffected, the egg white is milky compared to a raw egg. Whipping time is significantly longer for pasteurized eggs, but the final whip volume is nearly the same

Update: There was a culinary research paper released in January that I think resolves this issue (or see this blog post for a more accessible overview). It turns out that the protein coagulation in eggs is a function of temperature and time, rather than just temperature as was commonly assumed. So leaving your egg in to pasteurize for longer than the minimum required time will affect the texture. So use the minimum time of 75 minutes and you should see a significant difference.

Flash chilling is very simple. Just make sure you have a fairly large ice bath (ice and water that is at least 50% ice) and put the meat immediately from the heated bath into the ice bath. This will rapidly chill the meat prior to refrigeration. Make sure you leave the meat in the ice bath long enough for it to chill to the center if it's a thick cut or a roast.

1 How big should I expect the swings in my home fridge to be with normal usage?

The mild swings from opening and closing your refrigerator door a couple times a day aren't going to really make big difference. Just make sure you don't leave the door open for extended periods of time.

2 If I have a second fridge and the door rarely opens, what will the temperature swings be there?

There are a lot of things that influence the temperature of a refridgerator besides opening and closing the door. A refrigerator goes through cycles for chilling (and for defrosting) etc where the temperature varies. Some brands of refridgerators (i.e. Samsung) have separate cooling systems for the freezer and fridge portions so freezer defrost cycles do not cause swings in temperature in the fridge section.

Also, an empty refrigerator loses a lot more heat than a full refrigerator when the door is open. Storing plastic bottles of water or cans of soda and beer on empty shelves will actually make the temperature more constant over time since they retain more heat (or "cold") than air. Of course, if you turn a fridge into a beer-fridge, chances are that the door is gonna get opened a lot more.

3 Since the botulism concern is due to the vacuum, am I correct in thinking that this concern will disappear if I remove the meat from the vacuum to store it? Obviously, this approach would reintroduce all the normal safety concerns with storing cooked meat.

Sous-vide cooking should pasteurize the meat if it was cooked long enough and kill most . Keeping the pastuerized food that is sealed at a controlled temperature is going to preserve it for much longer than breaking open the seal and allowing any pathogens in before keeping it at the same temperature.

The most important thing is to follow the established safety charts for cooking times, temperatures, using correct flash chilling and then following the safety charts for storage temperatures and duration as well.