I don't quite see how this works.With 3E, i think the best way to fix it <snip> having the players invest actual in character time to dipping into any class.
If the other PCs continue adventuring in the meantime, in effect the player has to skip sessions or run a PC that is different from the one s/he wants to run.
If the time just gets handwaved, what's the cost?
If the GM decides that in the handwaved time that passes, event XYZ happen that render the players' previous engagment with the ingame situation irrelevant, how is that helping anything? If it wrecks the game, nothing achieved. And conversely if the players don't mind, then what was the cost for multi-classing?
If the idea is simply to give the GM fiat power over PC multi-classing, and to give the GM licence to impose some story-derived cost on the PC as a result (eg you trained as a cleric, and now you have a new suite of religious enemies), I think the rules would do better to talk about it in these metagame terms.
(Note it's different in a system that expressly has mechanics for passing time - so in RQ or BW, if one PC is training to boost some particular skill, there are rules that allow the other PCs to spend that time profitably in other ways - eg in BW, by making money working. But D&D doesn't have such rules - the only way to mechanically advance your PC is by actually playing the game.)