It sounds as if you have done the right things by digging the old dry well out and enlarging it. You mention that the soil is tightly packed. I assume that this does not mean that it drains well. If you do one load of clothes a day, for instance, the dry well should be completely drained before the next day. If this is true, then you should need minimal maintenance on the system. I would suggest that you put a filter on the discharge of the washer to help keep the lint from clogging the soil. Other than this you probably do not need any additional maintenance for several years.

If the water does not drain completey from the dry well, then the soil is not absorbing water as fast as you are putting it in. Since you have recently enlarged the dry well and therefore have fresh soil to absorb the water, I do not think Septic-Scrub would improve your situation. 

If you have any questions, please do not hesitate to call.