if its an olefin with that much soil in it, better to use a rotary, but it's going to wick. You won't be able to flush that amount of soil. The other methods won't disturb the deeper soil, so it won't be a factor. One of the reasons we say VLM doesn't clean as well, it doesn't affect the deeper soil which is what causes the after-issues.
If it can be vacuumed, with that kind of soil load I don't think you'll have enough time in the day to do it sufficiently
HWE is the most unforgiving; it won't win in a race. This will be as much a test of the technician in the contest, in the solution he chooses as well as his technique and settings, as it will be between the machines