If you plan to complete this bosstiary, you can only enter one boss per Stage 3.
There are three bosses but since you need to open their chest to reenter each lair and you can only open a chest each time, you can effectively enter only once per Stage 3.
The Stage 3 lasts for 5 days, with a 1 day of Stage 2 that makes it 6 days total. That would make it 300*3*6 = 5400 days or close to 15 years as a maximum.
But that is a maximum value. There is a trick to it:
Once entering the lair of one of the bosses, players have 20 minutes to be in there. The bosses respawn in 5 to 10 minutes time, so if you take a stronger team you can kill them multiple times.
Additionally, the entry to the lair is only denied after gaining experience from the Boss, so players can leave and reenter when at very low HP to gain time.
Effectively, with a good enough team you can kill the bosses at least 3 times in that timeframe. This would bring the 5400 days down to 1800 days, but I believe 4 times is achievable if the spawn rate of the server is good enough.
Rapid Respawn events and increased respawn areas do not affect boss respawn timers.
300 kills is a lot for them, but given this respawn mechanism 60 could be too low compared to others.