I think it's a very reasonable concept. But you're traveling in busy season and you may find that things like train tickets on the ideal trains are sold out. I'm going to assume that you are ending in Guangzhou because you already have a (nonrefundable) ticket booked on the 30th to Bangkok. So we'll run with that. Modify a bit and be willing to use flights.
14th Fly to Beijing
15-18th Beijing. You need more time than you've allocated. Night of 18th, book an overnight sleeper train on the Z43, soft sleeper is available and it's a good train.
19th-20th Xi'an. This is enough. Evening of the 20th, FLY to Zhangjiajie (airport code DYG). Right now if you go to www.ctrip.com there's a special for RMB 502, jump on this and book right now. Trust me, this is the connection to ZJJ that you want to do, not overland.
21st-23rd Zhangjiajie full days. Note that the Glass Bridge requires reservation so get to Beijing and look further into that. I'd split the ZJJ time as 2 days Wulingyuan Park, 1 days Glass Bridge and Grand Canyon.
24th Tianmen Mountain (adjacent to ZJJ city) for most of the day. Then overnight sleeper train to Liujiang. Right now soft and hard sleepers are still available on the K747 dep 16:28 and hard sleepers only on the T281 dep 19:14. On balance, I'd go for the T281 since it gives you the full day for Tianmen, stops less during the night, and arrives at a better time. This is a critical link and I'd book it asap.
25th Arrive Liujiang early. This is a new outlying station for Liuzhou city. Get a taxi to get you from Liujiang to Liuzhou rail station, then take a Liuzhou-Guilin fast train which is only an hour and not expensive. Should be able to buy this as a walk-up for next available, or buy in Beijing. Should be in Guilin by 10:00, at which point you can go to Rice Terraces or to Yangshuo.
26-29th Guilin/Yangshuo/Terraces area. You can decide how to split your time, but I'd minimize Guilin city. I'd get a fast train ticket 2nd class for the evening of the 29th from Guilin to Guangzhou. These tickets are selling out fast so I'd snap up something now or when you get to Beijing. There are also a few seats left for evening fast trains from Yangshuo (actually station is in Xingping) to GZ. Overnight 29th in Guangzhou.
30th Depart for Bangkok. Note: if your flight is later in the afternoon or evening of the 30th, you can do fast train from Guilin to Guangzhou this morning.
Train ticketing. Do it now or make it the first thing to do when you arrive in Beijing. You can go to any train ticket office (not necessarily at a rail station) and buy the tickets you need. RMB 5 surcharge per ticket, no big deal. Don't forget to take your passports.