How long for a oil to turn into sludge? The answer is far longer than you might think.
First off, sludge formation is as much a 'fuel thing' as it is an oil thing. All of the sludge tests that industry has used over the years to simulate sludge formation require a prolonged very cold start-up phase to ensure a lot of unburnt fuel gets into the oil. If you don't get fuel related nasties into the oil, you won't form sludge. And this is where things get messy. The industry has a fundamental problem in creating standardised sludge tests because everyday gasolines are 'too good'. You have to get someone like Haltermann to create a 'special' test fuel which contains stuff that 'promotes' sludge (I'm guessing something like stream cracked naphtha or raw coker naphtha) and some of these fuel are poor to the point of being ridiculous! Run the same test on typical pump quality fuel (full to the gunnels with antioxidant and ashless) and you just won't get sludge.
If you put aside the 'fuel thing', all oils WILL sludge eventually but it will take a lot, lot longer. All oils will oxidise if you expose them long enough to the effects of heat and blow-by. Base oils containing no additives oxidise quickest. Most oil additives, one way or another, mitigate against sludge formation. Of the different base oil types, very low VI Group I base oils have the greatest propensity to oxidise (because they contain the most aromatics). High VI Group Is (which you find in Europe) are better. Group II base oil (the commonest form of crankcase base oil in the US and Asia) are Group Is which have been catalytically hydrogenated and are very oxidatively stable. Synthetics are better still.
IMO, the chances of any US oil creating sludge in a 3k to 5k window are remote to the point of being non-existant.