Prices have gone up.
My sister was quoted by THAI in AKL for BKK-LHR at USD 960. She declined, but did do AKL-BKK for USD 870.
The THAI upgrade list that I have seen at the THAI ticket office had core prices in USD and THB equivalents. Payment is in THB in Thailand, USD converted to local currency elsewhere. You can buy airside at the Silk/First Lounge or at the transfer counters.
The earlier the better to try and snare a seat, and allow you use of the appropriate lounge - I'd usually turn up 3-4 hours prior, but that's just me!
Your option to visit a day or to before, a say 3-4 hours before, are probably the best bets as you'll have more time to arrive early.
Note that the biz cabin BKK-LHR on the overnight flight (TG910) can be quite full, whereas the noon departure (TG916) is often less full. Similar for First Class.
Cheers, TK