Do you get Home Shop Machinist magazine?
If not, you should track down an issue or two and have a good look at it.
There was a design serialized in that magazine, showing the making of a falling block, striker fired action, which they collected together and published as a stand alone book.
Village Press Publications is the publisher. Worth a look.
The square hole of the mortise is daunting to look at, but if it's a hobby anyway, you are in not a huge hurry. It can be dealt with by shaping, or by sawing and filing, but EDM (the money solution!) is by far the fastest and least risky method.
You soon learn, in metalwork, that you need a tool, to make a tool, so you can make a tool....etc.
If you can find a source of acrylic scraps (aka PLexiglass), they work very well for doing freeform cut and try machining. They also offer the ability to see what is going on inside while the cut is going on, allowing you to play around a bit while laying out inside machining set-ups, and seeing how things will work out.
If you keep to low pressure cartridges, the sky is pretty much the limit to designs.
If you can get hold of the DeHaas "Single Shot Rifle" series of books, there are a lot of means to an end.
One other method I have seen used, was to machine the action in two halves, and weld the halves together.
If you can weld, that may be something to look at.
Take a look at homegunsmith.com. Register and search for "falling block rifle". There are a couple different builds documented there.
Cheers
Trev