British Ryukyu

I'm looking for the best way to have the Ryukyu Kingdom become a Brirish protected state similar to how the Kingdom of Tonga was between 1900 and 1970 – basically the UK handles defence and foreign affairs whilst the local monarch mostly retains domestic control.

Easiest solotion seems to be the Bombardment of Kagoshima in 1863. Whilst the Japanese invaded the Kingdom in 1609 and annexed some islands two years later, in order to facilitate trade with China as a tributary state – it continued to send tribute to the Qing up until 1874 – the fiction was maintained that they were merely a tributary of the Satsuma Domain. Maybe the British are luckier, have a larger force, or for some other reason are able to achieve a decisive victory. As part of the negotiations the Satsuma are forced to renounce any claims over the Ryukyu Kingdom, with the British then entering into a protectorate agreement with Sho Tai. The fly in the ointment however remains China, finding a way to get them to renounce their suzerainty. If it was just a few years earlier it could have been rolled into the Convention of Peking but alas not. The next major agreement seems to be the Chefoo Convention thirteen years later, does anyone know of anything other agreements before that?
 
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