This is not an exploit, it is how queued orders work. In fact, you can do this even better (get it to work EVERY time, read further). Consider how the game works:
The worker chops are completed during the turn, not before or after. You can complete the chop yourself by clicking on the settler during the final chop turn (before it gets its turn "naturally"), and manually clicking Chop (which should display 1 turn left). Tada, chop is instantly (and manually) completed.
There is no real-time issue here. Every unit simply gets its "turn" to move. However, if the next unit happens to have queued orders (e.g. keep working on chop until done; another example is move to remote tile X), and it gets its turn, the unit applies its movement points towards that queued order (e.g. perform one turn's worth of chop; move one turn's worth of MP along the route to tile X). If a worker was about to complete its chop, and gets its turn, the chop is done right there & then. The screen just doesn't center on the unit, because it has no more movement points left. You can even force remaining queued actions to execute for the turn at any time by pressing Ctrl-A, according to Civ4 hints.
You can prevent the time-bomb easily, by turning off the worker's queued order (e.g. canceling the chop command with Cancel order) at the end of the previous turn. The worker will have cancelled its chop commands for the next turn, but it will still have done the current turn's worth of chop-time, e.g. 2 chop-turns! This is perfectly legal!
The next turn, you first switch production to Settler, then select the worker, manually click Chop again, and it should instantly complete, remembering the 2 previous "work-turns" already done on chopping! Then switch production to whatever else you were building.
The same way you can build a road instantly by moving two workers into a square and clicking Road on one, then the other. It is not really "instant" -- the workers invest work-turns into building the road -- but it shows that the order in which you move your units can make an impact on the game. AFAIK, all Civilizations were always this way.
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UPDATE: Just tried the "cancel-chop" method, and it works perfectly, even with no hammer loss from stale production. Cancel chopping at the end of the second turn, then manually finish chopping on the 3rd turn after choosing Settler.
What I did was (Emperor difficulty):
Build city, build warrior, and as soon as it reaches size-2, build worker.
Have Bronze working the same turn the worker is trained.
Switch production to work boat (to grab clam resource).
Settler-chop two forests while work boat is building (60 shields towards settler)
Workboat finishes and we reach size-3 same turn!
Unhealth from pop-3 relieved immediately by workboat/clam
Switch fully to settler production
Third chops finishes the turn after
Settler comes out 2 turns after third forest chop, and we are healthy/happy maxed at size 3! And a fast settler/worker pump.
Year is around 2640BC.
If we didn't use settler-chop, we would still be size 2 at this point. I think this is a very helpful maneuver for harder difficulty.
Another thing to try is pre-loading forests with 2/3 chops until getting the tech for an early wonder, then doing the final chop within turns of switching production to the wonder. I'll have to check how long the game "remembers" partially chopped tiles.