I'm not sure I'd do anything different really - I don't know of any other UK charts that cover the period. I would probably focus on the Missing Charts book (trying to correct as many errors as possible), given it was actually based on record sales. I'd perhaps try and collect the B sides as well, since I'm not convinced the A sides have been correctly identified - e.g. the other side of Turner Layton's 'Safe In My Heart' is 'When You Wish Upon A Star', which I'd have thought would have been a much bigger hit. That would double the work however!

I don't know how much I trust the sheet music charts on the Pop Music History site, without knowing exactly how it was devised. There are some real oddities there, e.g. Carter & Evans having the only charted version of 'One Dozen Roses', despite recordings by e.g. Carroll Gibbons and Joe Loss. I'd certainly never heard of Carter & Evans, and I doubt many people at the time would have done, given it was their first record! And then under 'You're Mine' it states 'sheet music only available', despite there being recordings by Oscar Rabin and Charlie Kunz (and probably others). And that's just from a quick glance at 1942!

You may be onto something with the artists being specified on the sheet music itself. There were certainly many 'versions' of each piece of sheet music, with different artists on the covers (specifying 'as broadcast by', 'as recorded by' etc.). Perhaps whoever devised the Pop Music History site had access to data showing what different 'versions' were produced, and then chose from those the artists that had actually released a record.