Are there any actually waterproof overshoes?

No. They have a great big hole in the top and another in the bottom is why.

My solution, untested I grant you is

Northwave GTX boots, so outside is pretty waterproof, paired with a pair of long Sealskinz socks, which are waterproof & breathable. These socks go as high as my calf, so avoids the issue of running down my tights and into the socks that way.

Sure, rain will still fill to shoes up in heavy rain, but the socks will keep my feet dry.

+1 Velotoze.

They are a bit of a faff to put on compared with typical neoprene overshoes, but they are certainly waterproof.  They've done me superbly well when raining (albeit only on my 12mile commute so no longer ride testing).

I'd imagine if you're riding for more than an hour your feet are more at risk of getting damp from sweat rather than rain!

Wetsuit boots with a rear zip are pretty water resistant, but have the advantage that even if your feet get wet, they don't get cold.

They can be had cheaply from diver's discount web shops or secondhand.

Often they have a tread on the bottom, so even after you have gouged a cleat hole in them, they still allow you to walk around a bit with racing shoes under, but without slipping over.

Buy a much larger size than your shoe size, because they have to go over an existing shoe.

This sort of thing:
https://www.diverswarehouse.co.uk/scuba/boots-and-shoes/prime-boots-with...

If you are not going to walk around, wetsuit socks are even cheaper. Remeber to buy a size much larger than your sock size.

On my mtb I wear Shimano gore text lined boots with long walking gaiters. The gaiters go over the top of the boots to stop the water going in. Result, totally dry feet. They also help to keep my feet warmer. Not very elegant or aero for on a road bike though

If its been pissing down ive put on a pair of socks, little plastic bags ( food bags ), then another pair of socks, my shoes and then Gore Bike Wear over shoes. 

Most important thing to do is keep the cold out rather than having bone dry feet. I used to wear plastic sandwich bags between two pairs of thin socks. They kept my feet well toasty. You sweat like a bugger though.

Last few years I've been using neoprene overshoes but with a rubberised outer layer.  Again you sweat a lot but it does keep both cold water and the cold wind out. 

I haven't tried it yet, but my idea is to get dry-suit ankle seals, and put them on upside down, with the upper end (originally the ankle seal) under legwarmers and the lower end (which would orignally have joined to the dry-suit leg) covering the top of Northwave boots.  It is essentially a marigold upgrade.

It's the old wet from the outside wet from the inside problem.

Tried many solutions and the best one, though a significant investment, were a pair of northwave GTX winter boots. That solves the waterproof and breathable bit, though you stil get cold (there are newere arctic versions which should do better there). The difficulty is then keeping the water out of the tops of your shoes. Best is gaiters (!) or long overtrousers which most cyclists hate on account of flapping. I have tries gaffer tape but that eventually got wet and gave in too. Like the marigold option. I haven't tried it but winter boots with something like gabba lights pulled over the tops of the top of the shoes would probaly work pretty well.

Hardcore winter MTBers use stuff like this: http://www.charliethebikemonger.com/45nrth-clothing-322-c.asp

No. There are ways to minimise water ingress though. Socks should be below the line of the overshoe, and tights should be over, not tucked under them. I read somewhere of using marigold gloves cut down to seal the top of the overshoe against your skin like the velotoze do. 

Velotoze are:

http://road.cc/content/review/160630-velotoze-tall-cover

not especially breathable though