What if you tally up the amount of delay you should have done, then when it gets to a big enough granularity where a sleep call would actually give you that amount, sleep.

Eg. Don't try to sleep accurately between the simulated cycles. Let things happen "too fast" for longer and do the delays in batches.

Not sure if this would wind up perceivably too bursty. Just an idea based on things I have seen in other domains.

For the record I don't think spinning is too bad of it's a very short duration, shorter than the scheduler will give you when you take your thread off the CPU.