Paint stores will normally use a heat gun to dry paint before showing it to a customer (cuz emulsion paints will change their color slightly as they dry).
Take one of those tiles down to any paint store and ask them to use their heat gun to soften that glue. When the glue is hot and soft, try scraping it off with a paint scraper or any metal scraping tool that's not sharp enough to damage the wood.
That's what I'd try first.
If it works, you might want to buy a better quality heat gun with electronic temperature control which will allow you to set the air temperature such that it softens the glue without scorching the wood.
I've already used a heat gun to remove the cork tiles and get most of the glue off, but there is still a tacky residue left, was thinking more of a liquid such as meths or white spirit.
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