Not too weird? I had someone tell me it barely resembles the original...which is true, but they didn't mean it as a compliment...
I had to listen to it again without the video. The video walks through the events and times perfectly to the video you were watching, so it seemed like it fit just fine.
I do agree that it sounds/feels wholly different from the original theme, but that can be chalked up the fact that the two have very different tones. The Chrono Cross version is fairly mysterious and subdued in harps and more delicate instruments. Your version is quicker (or feels quicker) and is larger and more boisterous, with brass and fanfare.
I get what the other(s) were saying in that it sounds very different, almost unrecognizable. I don't think they're wrong in that. But I don't think your rendition is bad or wrong, in fact, it's almost more fitting concerning the events that transpire: having reached the depths of Chronopolis, a confrontation with the heart of Project Kid in the Frozen Flame, and a final confrontation with Lynx/FATE. A lot all at once and worthy of brassy fanfare.
If
you don't feel confident in the vision you've laid out, you could always merge the two styles. Start loud and brassy and turn to more quiet and harpsical or vice versa. Or utilize the original as some sort of middle transition or something.
Either way, this version has my blessing. I view this as your interpretation through and through, and I am the first to say that any deviation is definitely NOT a bad thing.