Don't know your speakers (I have heard good things about them, though), but I love your CD player!
If given the choice, I would always opt for the separates. It is my understanding that the amp section of the 372 is identical to the 272, so no difference there, but the pre-amp of the 162 is a modest improvement over the 372, and includes a nice phono section, if that matters. But the biggest improvement comes from isolating the pre-amp section from the amp's power supply, and giving the pre-amp its own power supply. It just makes for a cleaner signal.
Certainly, price matters as the separates will cost more, but if the cost differential makes no difference to you, I would suggest you go with the separates.
Some gurus in my country said that C372 is basically the combination between C162 and C272. However, I think it's not true (like what you explained.) By the way, in my country, the price of C272 is 20% cheaper than that of C372.