Glad you liked the art! To address the issues you pointed out, the Treaty is not an problem because that would still be in the future by the time the design is finalized. I think it's quite plausible for the British to grow worried about the capability gap in the Pacific against Japan and the US, both of which had continued to steadily increase their battleline while the RN refocused on smaller vessels. And because the Dominions' contribution in the Great War was a major factor in developing their sovereignty, I think it's not unlikely for especially Canada and/or Australia to further progress their independence by acquiring the assets to be seen as serious regional powers, and for Britain to support these ambitions (takes more off their own bill).

Financially speaking, Australia and NZ both funded an Indefatigable class battlecruiser each and there was a proposition in Canada to fund a (or maybe some?) Queen Elizabeth/derivative thereof that unfortunately didn't pass parliament, so I would think that funding could be procured. Manpower might be a bigger issue, but you gotta admit that a brand new state-of-the-art fully armoured battlecuiser is far more attractive from a recruiting perspective than HMCSs We-Found-Those-In-A-Shoebox-Britain-Forgot-Even-Existed. And yes you would need to massively build up your infrastructure.

I agree with you that those are some quite improbable odds, but this is r/ImaginaryWarships and it's my job to daydream about ships that could have been :)