I'm guessing there are plenty of 973 regulars on this board who will chime in, but fwiw in the meantime, I've been to the Brussels airport several times recently, but took 973 only once and it was on a Saturday. Flight was packed to the gills with folks transiting from Senegal, and with large quantities of luggage well in excess of carry-on limits on quantity and size. Boarding and on-line luggage stowage were a real pain. Monday crowd may be different.
That said, everything leading up to boarding was a breeze, as were my other (non-973) experiences at the airport. The airport reminded me of a mini version of Schiphol in AMS in terms of layout of ticket counters. It was a bit disorienting at first and took me a couple of minutes to locate the correct ticket counter for UA -- if I'm not mistaken, the check-in for United flights was at the Brussels Air counter (sorry for lack of precision, my trips are running together in my mind). But there were virtually no lines to check in on any day I was there, and the lines that existed moved quickly. Security also moved very quickly.
I think that either transport plan you outline is fine -- in fact they will both get you there at approximately the same time. If it were me I'd do the train-hotel option, because I too hate getting up early in the am. And it's worth strolling around to see and have a beer on the Grand Plaz. I was cautioned by several people that the area around the train station, as in many parts of the world, attracts a decent share of pickpockets and muggers, so do be vigilant. But there is plenty of activity and lots of nice hotels nearby. Enjoy!