Oh well, if you're going to construct a whole new signalling system and loads of passing loops, then I'm going to construct a whole new network of track to run my urban rapid transit system on.
The trouble with monorails is that they are almost always a self-defeating concept. If you run a train on one rail, it falls off. And the simplest way to stop it falling off is to use two rails. Any other support configuration which confers static stability is considerably more elaborate, so all the supposed advantages of simple track, ease of construction, unobtrusiveness, and what-have-you, go out the window and you end up with this great beam that actually is wide enough to put two rails on if people didn't insist that you're not allowed to and have to do something more complicated instead. And the pointwork is a massive pain.
To make it work with one rail that is no bigger than a normal one, instead of cheating by making it as wide as a whole normal track, means giving up the idea of static stability and using some kind of dynamic stabiliser instead. While there are other possibilities, this almost always means a gyroscope. This is awkward in the case of a loco-and-wagons arrangement, as each vehicle has to have its own stabiliser, but that doesn't matter for an individual-pod type system as they all have to anyway.
They are also light, so the rail needs minimal bridgework to support it. If you have the supports at a close enough spacing - say by combining them with existing lamp posts - it can span the gaps on its own. So it is about as minimally intrusive as you can get - no massive great bridges, just a single thin bar connecting the tops of posts that already exist. And for large gaps - such as crossing a river - you can use a cable under tension.
The vehicles run on a pair of two-wheeled bogies, fore and aft, the wheels having a semicircular groove and running on circular-section rails (ie. steel tubes, like big scaff poles). Junctions are simply one tube meeting another at a merging angle, with slots like a frog to allow the flanges to pass and guide rails to ensure they don't try and pass some other way. Route selection is done on board the vehicle, by applying a slight rotational bias to the bogie pivots when approaching a junction to steer the wheels to take one route or the other. A pattern of magnetisation in the tube approaching the junction lets the steering system know when to perform and which junction it is; at other times the bogies are self-steering as per usual. If flange lubricators are needed the reservoir can go inside the tube.
The vehicles are both powered and balanced by a pair of counter-rotating force-precessed gyroscopes/flywheels. Because the precession torque is linear with speed but the stored energy goes as the square, they can be arranged to "run down" as far as their "battery" aspect is concerned while still having plenty of speed for balancing. When the speed drops below a given threshold the vehicle automatically routes itself to a depot where the flywheels are spun up again from a shore supply.
They also have considerably more torque capacity than is required for simple balancing. The vehicle, as has been obvious, normally runs on top of the rail - and the rail is up in the air out of the way. For boarding and alighting, the vehicle extends a set of circular steel bands which go all the way around the rail, and the gyros are then commanded to tip it over sideways at a controlled rate until it is hanging underneath the rail. To set off, the gyros torque the vehicle upright again, the bands are retracted and off we go. There is thus no need for stations and the pods can stop anywhere along the route. The bands gain their strength from width rather than thickness, and have bevelled edges, so that other vehicles can simply run over the top of a vehicle which is loading/unloading and do not have to wait for it. The bands are also loaded with a powerful spring which can bang them out in an instant if for some reason the vehicle does lose its balancing ability while going along.
The vehicle body is ovoid in shape, with the long axis parallel to the track, and is fixed to the chassis by two large ring bearings, fore and aft. It rotates in these bearings by its own weight to keep itself upright while the vehicle is turning itself upside down. There is a door in each side, hinged from the bottom so it can also act as a wheelchair ramp, and a longitudinal bar joins the ring bearings on both sides in such a position that it blocks the doors from being opened when the vehicle is in the running position.
The body consists of a front/upper transparent section and a back/lower seating section, which is opaque. Both are one-piece mouldings of suitable material, so there are no joints apart from that between the sections; the seats have an impervious, hydrophobic surface, and are shaped so as to have all corners smoothly rounded, no crannies, and no pond-like depressions. This is so that while the vehicle is at a depot having its flywheels recharged, it can at the same time be rapidly and efficiently cleaned with automatic hot water jets, and the water will all run off by itself leaving the seats not needing further drying. There is sufficient space in front of the seats to fit a wheelchair and turn it round on itself.
Intending passengers summon a vehicle by putting the coins to pay their (flat) fare in a slot provided in every post (a specialised robot vehicle comes round at intervals to empty the boxes via an emptying port at the top of the post). This means that if anyone decides to bugger up the system by ringing the bell and running away it will cost them. Route selection is done by means of a streetmap of the area with all the routes marked, laminated onto the inside of the passenger compartment with touch sensors embedded behind it; touching it at any point along a route commands the vehicle's guidance system to direct it to that location, stop, and turn upside down.