Engine-out procedures and eccentric forces on engine pylons

Long ago it occurred to me that a twin-engine jet running with one engine out
might be putting tremendous eccentric stress on the plyon and mounting of the
running engine (meaning stress not aligned with the normal thrust vector of
the engine). Today it occurred to me that this might not be true if the
pilots adjust the attitude of the aircraft so that it is flying straight
forward. The adjustments would create opposing forces that not only keep the
aircraft in level flight but also realign the stress on the running engine, as
if there were still two engines and symmetric forces on the pylons.

Does this make sense? If so, are there limits to how far an aircraft can fly
out of trim in such a way as to put unusual stress on engine pylons (even with
all engines running). For example, does yawing sharply in a large jet put
unacceptable stress on the pylons?

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