I don't think it's much of a setup problem. RFID is great technology. But it isn't necessary an exact science in terms of race timing. So it should never be treated as such.
Radio waves are invisible and don't exactly emit in a straight line in perfect alignment with a finish line. Position/location and speed of the target (and antennas) will determine when a tag is picked up. In most RFID setups, only 1 antenna port is active at a time, so there will almost always be a slight delay when tags are picked up by other antennas that are connected to other ports.
Most of these quirks are out of your control.
When precise timing is necessary, you should really be using cameras with you RFID setup (as there is no perfect RFID setup that will eliminate your core issues for XC). I use Finish Lynx and Identilynx as do most timing companies who time high stakes XC meets where exact precision is required. At the very least, you'll need a camcorder to watch for close finishes.