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For my money, one of the most basic errors you can make as a DM is to put the players into the quandry of "do I train? or do I finish the quest?".
This is always an unpleasant choice for the group, and its always the DMs fault that they're in that position. (its a failing of a DM in that the purpose of DMing a game of any RPG is to ensure the participants enjoy themselves; this kind of out-of-game catch22 makes that less likely, hence is to be avoided)
Firstly you've chosen to give out XP in the middle of an adventure; this is fine (I do it!), but has consequences (at some point a character IS going to level in the middle of a quest...)
Secondly you've made levelling a time consuming process. As stated, this is an OPTIONAL concept (not that there are _really_ any other kind in a game you DM...). It brings the consequence that the players need to halt the game in order to advance.
Having the group level at different points compounds this problem greatly; 2 points at which characters level up to 3rd means 6 weeks (game) down time, instead of 3 weeks if all characters can level together. [using your timescales]
Lastly you've then engineered conflict by also runnning time-critical adventures in an environment where advancement requires downtime.
Essentially; the players are in a position where they have 2 masters (progressing their character, and progressing the plot) and cannot serve them both (they need to use the same time to do either). You as DM have created this situation, so _you_ need to fix it.
Since you're in control of the timing (you both decide how long they need to train, and how fast they need to continue the plot) you can fix it either way.
Your options in the short term are to;
1; Reduce or eliminate training time
2; slacken or eliminate the timing constraint of the plot
3; put up with it, apologise to the players (well, I would feel the need to anyway)
In the long term your options increase to include;
4; don't give out XP except when it could be used (this can antagonise players who want to see their character grow each session; depends on the players)
but they really should also shrink to exclude number 3.
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As an aside; my group cured a DM of this. He seemed to revel in the concept of inflicting training (yes; training is something the DM inflicts, usually thinking it adds realism - all it really adds is a cost to advancement). Your character seemed to constantly need months of downtime, was usually beggared by training costs, and frequently you were supposed to delay training for months (real time) to finish adventures.
We cured the timing by ruthlessly dropping quests when we needed to train.
We cured the money problems by threatening to retire characters. "Why adventure when I can make far more money as a TRAINER?"
He got the message...