Issues

1. There's a reason I can't find anyone else doing this :-s

more practically

2. The cylinder head will need to be kept in place firmly enough that it won't be shifted by the increasing pressure of the compressed gas in the cylinder, yet will still reliably knocked out of the way by the cylinder, potentially the spacing of the exhaust valve could be such that the last X mm of cylinder travel is past the exhaust, 'super' compressing the resulting  air cavity, slowing the cylinder and softening the impact with the cylinder head? .

2b. Active management of those coils might be needed to allow the cylinder head to be knocked out of the way.

3. the cylinder need to reliably stop in the cylinder head position. perhaps the air cavity mentioned in point 2 could help?

4. how close would the intake/exhaust ports need to be? intuitively I feel there should be as little dead air around the cylinder head as possible, but thinking about it some more. As long as the cylinder head is close enough to the intake so the the departing cylinder doesn't create a vacuum before reaching it, it should be ok? also air trapped past the exhaust is wasted? (or does it help launch the cylinder head)

5. will a ball bearing actually work?

5a. Shape. 'maximum' efficiency would need a flat face so the isn't any dead air? although muskets/bb guns show a ball bearing is at least workable.

5b. Material. obviously needs to be ferrous. Linear motors that I've seen have magnets on them would the (bad terminology alert) 'magnicity' be strong enough without the magnets? or am I misunderstanding the issue???

6. Coil Timing. the cylinder needs to be tracked and the coils 'firing' at the correct time. need to read up but wouldn't the ball bearing induce a current in the coil which could be detected and reversed? I'm guessing this needs a micro controller.

7. compression effects.

as air pressure increases the cylinder is going to slow down. but pressure will vary through the 'orbit' and the pressure of the canister, is this going to create problems, certainly timings won't be able to be hard coded.

8. valve or valveless

it is quite possible to get away without having a no return valve on the exhaust port. Advantages: one less loss of efficiency. easier to run backwards as a generator.

Disadvantages: cylinder fighting against high pressure for the entire stroke.