My post master talks about the use of the mixmaster at the big sort facilites-- apparently no way around that here. Boxes dumped into a turning mass of boxes that are then one by one pulled out to dfferent sort lines. ( THis is how I remember him expaoining it-- might be off a bit, but still not a pretty picture.)
How are "non-machineable' or " do not xray " are handled??
*IF* done according to 'the book', they're NSM = non-standard mail - they would go into either a labeled sack or directly onto an APC (determined by size) at the receiving office. As an example; my dry-ice packed meat shipments go onto an APC - usually all by their lonesome - which is pushed back by the receiving doors so those poor employees aren't suffocated (by 5# of CO2 per box in a 1k sq ft building... ) If any other 'hazardous' materials come in that day, it shares the APC; if not, my boxes get their own carriage. Kinda a waste of space, but those are the rules Non-machinable (large or not rectangular) would just be the first thing on an APC; then anything they could fit would be packed around it.
Most employees I knew would try to 'specialize' and label an APC with non-machinable if there was enough going out to do so, or at least one half. (they have a center shelf that can be raised and locked into place) with stuff such as bags of 'do not Xray', registered bags, express mail, etc. - if not, it gets filled with anything else (machinable or not) that fits and it's up to the sort facility to figure out if it's machinable from the bag tags or box labels and divert it to the correct sort
Small items go in a sack, but that sack is quite liable to be tossed around, and whether sack or unwieldy object, it's still going to be put on the APC in any way it will fit - it's just that the label diverts it to hand-sort at the sorting facility. At hand sorting, the bag is dumped onto a conveyor again. "This End Up" is really a useless notation if the box can be held in one hand. Really, the only thing that gets anything like white glove handling is live animals (preferably cute ones that make noise) and things that require a DOT HazMat label.
Your postmaster's description sounds like parcel post sorting - I think there's a few videos of sort facilities in operation on YouTube - it's really rather frightening! Parcel post for small items at the receiving office is no more comforting; they arrive in a canvas wheelie bin & are sorted into smaller ones for each route - but there's a reason the sorting task was referred to as 'throwing parcels'... (in fairness, sorting letters is also referred to as 'throwing mail') Priority mail boxes were designed to best fit the equipment; they actually get better handling than most containers because a specific number will fit in a specific way in an APC. Most 'live chick' boxes were also designed to fit that equipment.