The only way I know of to get around this, is to break the reservation into two separate ones of three and four days. Have them book the first part and pay now. Manually block the remaining dates on your calendar until such time as you require them to pay the second part. Then send them a special offer for the remaining days of the week.
If you do it this way, the weekly discount will not be applied, so you will have to do a special offer to get the numbers correct. Also note that your ability to recoup on cancellation policies can be negatively affected by having two separate start dates.