Britain saying it was reluctant to colonize an area doesn't really mean shit.
Because Britain wasn't a hivemind and speaking of an official british opinion is misleading when you had forwards and backwards factions re the empire.
I can't speak for this particular example but I can speak for Africa, where consistently you had British officials say they aren't going to colonise this area and then they did. A good example would be the aftermath of the second Anglo-Ashanti war wherein the Foreign Office issued a memo to all their West African governors to not start any more fucking wars and that Britain was going to pull out of west Africa entirely, with the possible exception of Freetown.
And that just didn't happen at all.
What you saw throughout the British Empire in the 19th century, was the treasury going 'no this campaign is expensive and this land is not worth it, pull back' and that maybe lasting for ten years at the maximum before the 'paint the map red' side wins.
They won largely because the people on the ground wanted it. If you read the diaries of British army officers, they are constantly moaning about London not giving them the support they wanted to but then constantly just doing it anyway, by rousing public support, or convincing private backers to fund them, or starting the wars themselves or just lying to london about what has happened or bribing politicians or fearmongering about the french taking it instead or whatever works. And there were always people in Whitehall who were happy to give them what they wanted.
I do actually think the era of new imperialism can be avoided but the system was self perpetuating, once you have created the apparatus for a colonial war, it gets used and it spurs on itself. Governors on the ground and certainly settlers on the ground would constantly push for more land and more slave labour provided by new subjects.
As you say, focusing on statements within that system saying 'steady on lads' is a red herring because while there were voices who wished for an entirely informal neo-colonial empire, they didn't get their way long term. So you can't just have them be listened to, you need to change the system itself in drastic ways so that it has different people in power.
Having said that I do think in a world with a less extensive era of new imperialism, for whatever reason, Burma is probably one of the countries likely to be mostly untouched.
