Alas, no production electric folding bike has your whole list. On the other hand, the production folding e-bikes are mostly well within your budget.
Converting the S8i can be done; Add-E offers a kit which will work. They’re about the only option, though: BionX kits work only with derailleur gearing, so no Gates belt drive; Electric Bike Outfitters leaves the internal gearing intact, but will instead will replace the front wheel, removing the light-powering dynamo.
Add-E’s kit is LOUD; aside from that, it’s a surprisingly effective add-on motor. The battery is easily removed and charged. There are two motors available, a 250 watt for about $1400 AUD and a 600 watt for about $1800. If bought with the bike, I’d expect any shop to do the installation free of charge; otherwise, it shouldn’t be more than $50-100 to get it set up.
If you are willing to make some tradeoffs, there are a number of interesting electric folding bikes out there.
Mando makes the Footloose, fenders, entirely enclosed drivetrain. It has no rear rack; it would be possible to add a seatpost-mounted rack, with its commensurate limitations. Also lacking integrated lights. OK, not really close, but it’s got a great look.
The GoCycle G3 is closer; with the offered Commuter Pack it’s got everything but the rear rack. A post-mounted rack is also the only real choice here. The G3 has a nice design, with the drivetrain sealed up, full suspension, and a spare, space-age frame. Unfortunately, the package comes in at a little over $7000 AUD.
Blix’ Vika+ is not a high-performance bike, but it is nicely kitted out: fenders, a chainguard (not full-length), a rear rack, head and taillights powered by the same battery as the motor, which can be charged on or off the bike. About $2200 AUD.
Daymak has the New Yorker, rack, fenders, integrated light set. It’s a little low-rent - lights have to be switched on and off by hand. It performs pretty well, but you might expect to need a bit more maintenance. About $2000 AUD.
Enzo’s eBike has everything but a full-length chainguard, about $2300 AUD. It does have a double-sided chainring guard and a derailleur guard, which should mitigate the perils of grease somewhat.
For performance, you may be best off sticking with the Verge and going with the Add-E kit, if you don’t mind making some racket when running the motor. Second choice, among the fully-accessorized, I like the Enzo; it’s got very durable, low-maintenance construction, solid parts, and it folds up nicely.
Sorry I can’t offer more than compromises. Hope this helps.
Edit: the new Pedego Latch is everything but lightweight.
Folding list: fits riders to well below 5 foot, and as upright as you would like to be. There’s a three-speed hub rather than the Verge’s eight-speed; the gear range is similar, with fewer choices. It is about 23kg, with the battery. Folds in thirty seconds, and is equipped with the Gates belt drive and a chainguard, the latter here serving pretty much just to keep your trouser leg out of the gearing. Low maintenance - the most tetchy part is likely to be the electrics; Pedego is all-electric, and has an excellent reputation. You will need to buy a bell.
Electric list: runs with or without power assist. Battery easily charged on or off the bike, and easily removed for same. Front and back lights run from the same battery as the motor. Back rack and mudguards. No front basket, alas.
The clincher: Pedego offers the Latch in a glorious lime green, frame and wheels.