We're talking about Chinese mining pools right? Not all Chinese miners are solo mining. Most of them are in mining pools, which use Stratum and GBT
Do you have something that shows that the pools they're using use Stratum/GBT?
F2pool uses stratum. They have their miners connect to stratum+tcp://stratum.f2pool.com:3333
BTC China uses stratum. They have their miners connect to stratum+tcp://stratum.btcchina.com:3333
AntPool uses stratum. They have their miners connect to stratum.antpool.com:3333
So yes, Chinese miners are using stratum for their pools
In either event, pool-based mining, which they clearly use, does not require the download of the transaction data. The block size does not matter. You can verify this yourself - connect to any of these pools and watch the data transfer - it is a teeny tiny fraction of the full transaction data volume.
Even a dial-up connection can handle that kind of bandwidth.
Red. Herring.
Even so, Chinese miners have their full nodes inside China. While you say that "they can just move their full nodes outside of China" that is easier said than done.