Need help with dizzy problem

1976 XB block with a 82 XD carby head. Factory Bosch points type distributor. The engine started to miss intermittently. Problem is now getting worse.
When I push down on the dizzy cap the engine smooths out. I have checked primary wiring to the dizzy, ignition wires, plugs, cap, rotor etc. All are good. When I had the cap off I was able to raise/ lower the dizzy shaft approx 7mm. Is that normal or has something worn out or broken in my dizzy? It seems that the shaft moving up and down that much would change the engine timing as the dizzy to cam gear engagement position would change.
Question number two. Can an electronic distributor(non points type) from a later engine XE XF be fitted to the 76 block. If yes, what parts would I need to order to make the conversion work properly.
I am located in the US, so getting parts shipped to me is time consuming and returning an item is not economically feasable due to shipping costs. Really need some good info here so I can get the correct parts to repair the problem.
Any help will be appreciated in helping me figure out the problem.

You've lost the circlip that holds the upper shaft section to the lower (driven) shaft. This circlip fits under the rotor button, under the oiling felt.

Providing the cam gear and driven gear are in good condition, TIG weld the existing driven shaft to just under the baseplate of the electronic distributor's driven shaft. Preliminary machining would be to leave a cylindrical tip on one section and receiving bore to the other, with a deep V-groove for weld where they mate. Silver solder or braze might work, too. Rebush or ream the electronic distributor for the larger shaft.

Option B would be a reducing bush pressed deep into the engine block to carry the electronic distributor's reduced diameter nose.

There will be some self-evident light mods to the hold down aspect; a dry fit will show what's needed. Assemble with new moly grease or similar oil-compatible lube.

I would spin the new dizzy up on a Sun machine or similar to see what the curve needs doing to it.

Adam,
Thank you for the speedy response.
New Crow cam and Crow dizzy drive gear with less than 3,000 miles on them so the gears should be fine.
Let me see if I understand your instructions correctly.
Option 'A'
Purchase a carburetted XE distributor.
Cut off the bottom portion of the shaft.
Weld the bottom portion of my original shaft to the new one.
Modify the hold down to secure the new dizzy casting.
Option 'B'
Purchase XE dizzy.
Install bush to size lower dizzy support bore to smaller diameter.
Modify hold down to secure new dizzy casting.

On option 'B', can the bushing be installed in the engine block from the top or would it require the engine to be disassembled and the camshaft removed to instal the bushing?

Is the XE dizzy a stand alone unit with control module integrated or is the control module located outside the dizzy like a US production Ford? I guess I am asking what parts do I need to purchase when I email an auto parts store in AU and tell them what I need sent to me.

Your "Option B" bushing would be pressed in from outside the block, meaning it's do-able in situ.

The units are fully self-contained, with the driver module under a little metal lid attached to the side of the distributor body. You could ignore this part and run a shielded wire pair from the pickup sensing coil, directly to something like an MSD module if desired.

Why not press a sleeve to the bottom of the distributor shaft?

Here is another idea... why not go for multiple coils - then you can be rid of the dissy, needing it only for oil pump drive. A ignition-only megasquirt or something would do the trick. Might also be a cheaper option in the US.

Good question.
As the dizzy can be worked more easily on a bench opposed to the bushing being installed in situ in the block. Any reason the bush to enlarge the diameter of the dizzy housing can not be installed on the dizzy? It seems to me it would accomplish the same result whilst being an easier operation working on the dizzy on a bench after it is removed from the engine block, opposed to trying to fit the bush in the block.
Any comments on this subject are welcome.

From memory, there's only 20-25 thou difference in the shaft sizes. That would give you a sleeve of 12 thou or less.

Making it a tight fit on the shaft runs a distinct risk that as the motor heats up, this sleeve will become unbonded. Were it pressed into the block, expansion would be in the direction of its existing "bond".

Hope this helps!