Hrm. If I understand correctly, you have ONE segment field, and it can contain EITHER the 'business' date, or the 'technical' date, which makes searching for a particular document difficult.
If I understand your problem correctly, the best recommendation that the two dates be stored separately, so that a user can search on the field of their choice (either 'business' or 'technical' date).
If that's not possible, I'd increase the range of the default query to cover a range of dates that would catch BOTH dates, or require that an additional field (something that is 'mostly unique') be queried at the same time, and add an index to that field.
Of course, this means you're doing MORE work, not LESS work (like you originally asked).
If this can't be solved simply, I'd start looking carefully at ways to optimize your database performance to make the queries move a little more quickly.