Welcome back Bruno! What you are getting is a lot of reflected sounds off of your hardwood floor. I too, have a very similar sized room to yours, about 19 x 13 with double garden doors and 3/4" hardwood flooring....I don't think the species really makes any difference but it's African Walnut for the record, lol. So anyway, I've got an 8 x 11 thick pile wool rug in the centre of the room which helps considerably with those first reflections, although I put it there with the original intention of protecting the hardwood in the main traffic area. You don't need to completely cover your hardwood, but I would put either a 7 x 9 or perhaps an 8 x 11 in the middle of the room...it still shows plenty of hardwood around the outside and personally I think it looks much nicer than just all hardwood, but that's up to you. Curtains will most definately help too, I have a combination of aluminum blinds framed with curtains. Something else you might consider to reduce reflective sounds is "hanging" a decorative rug as well.
A rug on the floor is where I'd start though, I would probably try for a rug width similar to the spread on your towers(7 or 8 ft). I believe some people have been successful raising the speakers up a few inches as well but I've not tried this myself.
Also, I'm using the rubber feet...I wouldn't even consider using the spikes unless they are not in direct contact with the hardwood.
