I would start by doing some simple link-time tests, send a character to a unit
and have it respond back, and measure the loop time. The deal with XBees [at
least the 2.4 Ghz units] is that they use packet transmissions, and they send those
packets embedded in the zigbee protocol wrapper. They also do some band checking,
with fallback, before doing a transmission. You need to know how long that all takes.
Secondly, it doesn't sound like you need Faludi's book, but you should realize the
schematics are all wrong. He is interfacing a 3.3V device [XBee] directly to a 5V
Arduino, although he does mention using 3.3V power to the XBee.
Another problem is that you probably need to configure all 3 XBee nodes to broadcast
mode, as opposed to one address to another, which only allows 2 nodes. The remote
broadcasts the sync to both other nodes, and then the 2nd node can broadcast
to the 3rd node.
I would set up an address in "software" for each device, so they can filter messages
meant for them individually. Any way you go, you will have a problem that #2 may be
transmitting to #3 when the sync signal comes in. Personally, I would use handshakes
[Ack response by receiver] on all transmissions.
Also, for 300' range, you're probably best going to the 900-Mhz units, as the 2.4Ghz
XBee-Pro reliable range is only around 300 feet for general use.