Your issue may relate to problems in the brewing process that go back into the mash that are getting cleaned up by the yeast after a second conditioning phase (the first being post-fermentation in your conical). You could try conditioning the bottles warmer and see if the conditioning phase shortens. On the other hand after the bottles carbonate you could try cold conditioning to see if that helps drop out yeast and other sediment in the bottle and give you a cleaner, clearer beer. The conditioning temperature by itself likely is not the culprit but rather a proxy solution.
Look at your bottling regimen. Are you introducing oxygen unnecessarily that requires the yeast to deal with the oxygen during bottle conditioning? That would certainly reactive the yeast and give you bottles with more yeast in suspension with the yeast bite that tends to mute a lot of preferable flavors in the beer. Are you picking up too much sediment that is suspended in the bottles for some time?
Are you using a powdery yeast strain and not removing most of the yeast by cold crashing, finings, etc.? The more powdery the yeast the harder it is to get that yeast to drop out in the bottle without cold aging after the bottles condition. You can also look at whether your mash has sufficient calcium to help the yeast floc out.
Is fermentation healthy? Are you pitching a healthy volume of yeast? Properly oxygenating and providing sufficient nutrients? If the fermentation is stressed then you likely end up with off-flavor compounds and the precursors to off-flavor compounds that need that longer period of time to resolve. Sometimes a flat beer that can hide of these compounds that become detectable in a carbonated beer as carbonation articulates flavors.
Otherwise it could be any number of other factors such as issues with your water supply, recipe choices, mash process, etc. but it's hard to guess at what individual factor may be responsible. I'd look at the easily identified issues above first.
I disagree with what has become canon in homebrewing that you have to leave your beer in the fermentor for a month or more followed by six or more weeks of bottle conditioning. There's nothing wrong with aging beer or enjoying your beer at whatever age you find it best. I age lots of beer for far longer than this. However, with good brewing practices there is no reason why you must wait two and a half months for your beer to be ready especially if it is not your goal to wait that long. The loudest voice of this paradigm is a guy with clearly terrible brewing practices who decided his time has been better spent preaching and developing a congregation this garbage than improving his brewing.