ZDC ARTCC Controller reported situation of high volume of traffic and complexity resulting in an unsafe situation with aircraft unable to descent due to traffic and the sector not receiving proper spacing of aircraft.

Narrative

There was simply way too much traffic given the complexity of the situation. The sector was red; and not enough was done to mitigate the situation. Northbound TEB/BED aircraft could not descend due to head on traffic southbound on Q97/Q167; and if you wait until the routes diverge; they could never make their exit restrictions to ZBW. Additionally; the need to space with HEADI traffic from 58 at the very last second meant that the complexity of 59 was extremely high. When the VOLUME was also allowed to go extremely high (and even beyond the established limits); the sector became very unsafe.The TEB/BED arrivals through Sector 59 via HEADI going via Q167 YAZUU HEADI keeps them too far east; and creates too much complexity with southbound traffic in the thirties from ZBW; when there is volume in the sector. The routes need to turn west SOONER than YAZUU; much sooner. Realistically; KALDA Q97 HEADI is likely what is needed-- I'm not sure the intent behind keeping them east; but it's worse than just letting them run up Q97.Additionally; the challenge was worsened by the lack of proper spacing being provided to Sector 59; and the aircraft being delivered in the forties. Some of those aircraft need to leave at FL250; and there is no way to descend them cleanly-- as such; Sector 39 should get all TEB/BED types down to at LEAST FL370 or lower; and it is likely that the complexity that action incurs to 54/39 that Area 3 will need to handle some of the TEB spacing for them.And finally; since not ALL of the complexity can be resolved; the total volume simply must be reduced. The MAP numbers for 58/59 in this configuration must be reduced from their current values to ensure the sector remains safe.