An egg is good until it is bad and it will be obvious when you crack it, that it is bad.
I don't propose you keep all your eggs for 6 weeks on the kitchen bench, a cooler place is better but they don't need to go in the fridge. It was just to let you know that they do keep incredibly well and not to throw them out just because they have been sitting around for a few weeks.
The way many people, including myself, test them if they have got old, is to put them in a dish of tepid water....if they bob to the surface they are dubious and care needs to be taken when cracking them open, but even floaters are sometimes still edible, although I usually scramble them and feed those to the cats or chickens. If they are really bad, believe me, your nose will detect it.

. The freshest ones will lie on their side on the bottom of the bowl and progressively start to turn round end up in the bottom as they age until the air sac becomes large enough for them to eventually bob to the surface and float. Not that I am suggesting you leave them in a bowl of water for weeks, but just that when you test them, that is what you find happens.
Good luck with your next bread and butter pud.... it is one of my favourites! Have you tried using cinnamon and raisin bagels instead of bread or brioche is really naughty/nice. I look out for reduced bakery items at the supermarket that I can use for it, like the above or teacake loaf. It is better made with stale bakery produce anyway as it holds the texture better.