How high were you actually? approx track miles when u were cleared to descent below 340?
Anyway.......since it's ATC "fault" cos they kept u high and restricted your speed...just inform the ATC that either u increase speed or due to the restricted ATC speed, you will be requesting extra track miles to lose height.
Depending on how high you are....increase speed might not be enough to regain profile. In that case, just request extra track miles to lose height. They won't force you to do an approach if you warn them you are too high.