When you have more cuts than you are comfortable with, tire is dried out and cracking or you know that threads are about to be exposed. Tread pattern wear has never been much of an issue, at least for me. I don't mind if the pattern is gone and I am riding on patternless rubber. When I start to get worried abut the the tire I start double checking my repair kit.
That's 3900 miles. I've never been able to get that many miles out of a rear tire, not even on my single. I suppose I might be able to come close on one tire by running it on the front for a couple of thousand miles, then rotating it to the rear, but I wouldn't rotate a tire from rear to front after it has "squared off".
My vote is to replace them before they start causing problems.
Suggest you buy a couple more sets of those tires! That is terrific tire mileage for a tandem . . . especially the back wheel! What brand/model/size tires are they?
Do agree, check tires closely for cuts/dryrot/checkering of sidewalls. If thread pattern is worn and is now smooth . . . still good to go.
Most tires now are much lighter than in the 'old days' due to thinner sidewalls/less rubber/kevlar beads.
Normally get around 2,000 miles on a rear tire and up to 3,000 on a front tire nowadays on our tandem. However, depending on luck, brand/model of tires, you experience can/will vary!
Pedal on TWOgether!
Rudy and Kay/zonatandem
6300k.... on a rear tire? Let me guess: you're riding a 26" wheeled tandem with some really inexpensive, long-wearing off-brand OEM tire like a Cheng Sing (aka, CST)?
Regardless of what brand of tire you're using, if you've been pleased with the performance (comfort, grip, durability), I'd suggest you try and pick up a spare and keep your eye on the center of the tread of your current tire for signs of wear-through to the casing. Once it does wear through -- or if you start getting cuts in the tread -- move your front tire to the rear and put the new one on the front.