A go at a Foamie

Weigh the blades separately and sand the back of the heaviest one.
Here's another way, use screws and nuts to secure the blades. Tighten so they're stiffish to move, run them up on the motor to about 60% (so they line up nicely) then find some way of mounting the whole thing in a prop balancer.

That's what I do - tighten up the pivot bolts until the blades are almost but not quite locked, then press the backplate down onto a flat surface, and adjust the individual blades so the tips just touch - then use my regluar magnetic balance.

I've read Magpie's comments several times, and cannot understand what he is saying about a vibrating fixing plate.
If something is fixed -  not moving - it cannot vibrate!

With no power connected, no prop fitted, etc, but back (mounting) plate on - if you turn the motor with your fingers does something catch? The only resistance you should feel is the slight 'cogging' from the magnets in the rotating bell.
Have you mounted the non-rotating part of the motor, with the wires and coils - correctly?
How does that part fasten to the fuselage? Some have a four-legged 'star', while others - the very small ones - have a thing like a top-hat that the motor has a neck that fits into, and locks by grubscrews - usually at 90' to each other. The 'star' or the 'top-hat' should be fastened to the mounting plate on the fuselage - usually F1 or the extended motor 'box'.
Have you used the correct-size top-hat? The motor neck should be a close sliding fit. With the grubscrews tight, it shouldn't turn, rock or wobble. The four-legged star type should screw to the non-rotating part of the motor with SHORT screws that don't foul the windings or the bell magnets. (they are usually provided with the motor - and are typically 5mm long!) Wth those tight, the motor back-plate cannot move. (use a drop of releasable lock-tite on the screw threads, so they cannot work loose over time).
With NOTHING attached to the motor, when you power it up, does it vibrate? It shouldn't.

When you power up the bare motor, it shouldn't vibrate at all - if it does, is the magnet bell wobbling? That could indicate that the motor bell is out of line on the motor shaft,and you need a different motor. You MIGHT, with a lot of luck and patience- manage to straighten it out.
OR it could be that the shaft is bent just past the bearing, so the bell appears to be wobbling. If you can get one, the shaft can be replaced.
Is the shaft bent past the end of the magnet bell? Spin it, and see if the tip of the shaft is oscillating.

If there is no problem here, then the vibration HAS to be an out-of-balance prop, hub, or spinner.
You say that you cannot get a clear indication of prop balance. What are you using to balance them?
Don't forget that static balance, and rotating balance - are different. That is why a garage spins the car wheel to get it balanced, by adding weights to the rim, when you change a tyre, and the balance will be in, or out, depending on the rpm's! It is rare to get a balance that is spot-on at all rpm's.

You want a balance with as near to zero friction as you can get. Mine is a U frame, with a magnet in each upright leg,and a steel pointed shaft that is not quite long enough to touch both sides. (The magnets try to pull the steel shaft towards themselves, so it is effectively suspended in free space) On the steel shaft are two rubbery cones - pointing towards each other - that can be slid along the shaft..
The prop being balanced is trapped between the two cones, the points of which slide into the prop bolt-hole. Thus the steel shaft is centred in the prop, which is free to turn on the assembly, but not within the cones. The only contact (friction) is where the one point of the steel shaft is touching the magnet (the other end doesn't quite touch).
The heavier blade will always drop down - pulled by gravity.
The steel spindle is so free-running that a light breeze will spin the prop - so the balance cannot be used out-doors - or in a room with windows open or a fan running!

That looks like the folding prop severely out of balance.
If you make a U shape out of wood and bolt a Razor blade at the top of each leg you can balance the prop by putting a piece of correctly sized Silver steel rod in the back of the hub and use a long screw in the nose, put the whole thing on the blades and check the balance.
I have to agree that back plate doesn't look 'fit for purpose'.

I have no recollection of seeing that photo before - perhaps I missed it?
If Magpie takes the prop nut off, and withdraws the clamping collet, there is a hole through the prop so it can be balanced the regular way.
Then - if the clamping collett, washer, and prop nut are fitted to the motor - without the prop, THAT can be checked for vibration. They are often made of very soft metal that bends easily.
If that is clear  then put the spinner on, and check again!

That motor mounting thing looks awfully flimsy. I've not seen that type of mount before, and as stated, if it is intended for indoor ultra-light models - obviously it cannot take the stress.
It looks as though the three wires feeding the motor have been mangled when the motor broke free, so I'd suggest you carefully untwist them, and ensure that the insulated sheathing of each one isn't damaged. If two wires should short  under power - goodbye speed controller. If one is broken, that would give the motor 'the staggers',and it could be that that broke the mountng. It's timing would be upset, and it would try to run in both directions at the same time!
Sometimes - buying cheap isn't the most economical!

The motor for Q's Fokker is clearly of the four-legged star mount variety. It's on the bench behnd the fuselage.