Pretty sure I've had the same issue. Gone through the same process as you trying to pinpoint it - I've never had an infection in fermentation, nearly all of my batches (over 8 months of AG brewing) have tasted excellent (imo) - or at least what I was after or expected - out of the fermenter. But once in the bottle, they develop the same specific off flavour. Sometimes they stay good for the first week then go, other times it presents right away. I've used spring water, tap water, distilled water - same problem develops. It's not DMS, diacetyl, band aid, metallic, phenolic, esters, green apple or any of the other most noticeable classics. I upped my bottle/gear cleaning regimen for a recent bottling batch (again which tasted great out of the fermenter), replaced main tubing and had a relatively new siphon, and I bottled it in a different location (helping pinpoint if my kitchen is just a mess and the culprit) - all to have that same flavour still develop. I was told it might be oxidation/cardboard - and other than cardboard being difficult to actually taste - it's even more difficult not exposing homebrew to air. I think I'm clean/sanitize decently, and am as quick and gentle with transfers as possible - but can't say.
All to say I feel your pain. As others have mentioned, I'd heard wild yeast presents as overcarbonation - which IS something I've had consistently. So this could be it, but I have trouble knowing where wild yeast is getting in - other than through air into my bottling bucket. Certainly possible, but if it was that easy I'd assume every record in the annals of homebrewing would be plastered with people talking about it - something I have NOT found or seen. So, I have two batches close to finishing and do not know whether to buy kegs and throw bottling to the wolves, or try yet again...
Do let me know if you have any breakthroughs; I'll do the same.