Bogs: well, time-wise you definitely can - if I'm mathing correctly it takes a total of 1 day, 8 hours, and 40 minutes to brew each egg and the components thereof. But that would depend on you having enough starting mats.
I'd start by crunching out the total quantity of mats you have versus what you'd need to do all the brewing - focus on what transmuting needs to be done during times you're active on the site anyway and can toss in a new item every half-hour (or when you can easily get to a computer and just set a half-hour timer). Brew the longer components overnight and save the eggs themselves for busy days you wouldn't be actively FR-ing.
Coli is always good, but personally I'd forget the eggs from there and focus on how you can make the most cash the fastest (train fodder if that's a thing you do or farm for valuable but more predictable drops like Fanned Cockroaches) and bank the t/g to buy any eggs you're short on. Getting any to actually drop would be a nice bonus but can't be counted upon.
Don't forget your fairgrounds - you can make more than 2 million treasure that way in a month, which can net you 6-ish eggs. G&G is the fastest, look up the hacked/broken way to solve it.
Scavenging is always an option, but whether it's better to roll the dice for eggs there or make more profit for your egg fund in other disciplines isn't something I can advise on, I never gather linearly/logically enough to have a good perspective there.
Re: 10 eggs challenge (?)
I'd start by crunching out the total quantity of mats you have versus what you'd need to do all the brewing - focus on what transmuting needs to be done during times you're active on the site anyway and can toss in a new item every half-hour (or when you can easily get to a computer and just set a half-hour timer). Brew the longer components overnight and save the eggs themselves for busy days you wouldn't be actively FR-ing.
Coli is always good, but personally I'd forget the eggs from there and focus on how you can make the most cash the fastest (train fodder if that's a thing you do or farm for valuable but more predictable drops like Fanned Cockroaches) and bank the t/g to buy any eggs you're short on. Getting any to actually drop would be a nice bonus but can't be counted upon.
Don't forget your fairgrounds - you can make more than 2 million treasure that way in a month, which can net you 6-ish eggs. G&G is the fastest, look up the hacked/broken way to solve it.
Scavenging is always an option, but whether it's better to roll the dice for eggs there or make more profit for your egg fund in other disciplines isn't something I can advise on, I never gather linearly/logically enough to have a good perspective there.
Good luck!