The first several rounds fired eject as they should but as the barrel/cylinder heat up, the cases bind in the cambers and will not eject without the help of a light tap with a smith's hammer on the ejection rod. Only two of the chambers expand enough to cause the problem. I don't trust myself enough to use a finishing reamer but I was thinking about using some medium grit lapping compound on a mop (chucked into an electric drill) and see if that might solve the problem. Is this a good idea?

Not really. With the mop you have no control of keeping the chamber walls straight and true. If you search the forum you will find excellent tutorials on using the finishing reamer. If you are worried maybe an experienced friend or a local Smith can help.

Polishing out the Chambers (with basic cleaning tools) of S&W .22 Revolvers usually only elevates the problem for a dozen or so shots. The only way to permanently solve this is to get the proper Reamer from Brownell's and properly ream them.

This procedure is not difficult however does require mechanical skills as well as confidence and common sense. If you are not confident, let a qualified and recommended Gunsmith (or at least a Master Machinist familiar with S&W Revolvers) do the procedure. Again, not difficult - but needs to be done correctly like anything else.

HINT: Keep the Chambers as clean and as free from chips and debris as possible and use plenty of cutting oil. READ DIRECTIONS THOROUGHLY!

PS: The Reamer sells for about $150 - $165 so if this is your only Revolver you intend on working on, it might actually be cheaper to let a GS who already owns the tool, do it.

Invest in a Flex Hone manufactured by Brush Research and sold by industrial tooling suppliers or Brownells. These are regularly used to polish ID's to improve surface finish in both gunsmithing and industrial applications. Easy to use if directions are followed, almost fool proof, and you will tire of holding the drill motor providing power long before you will damage a chamber ID. Use the search function and you will find a similar thread earlier this year. Personally, I have used Flex Hone products on shotgun chambers, rifle chambers, and revolver chambers, in addition to many metal working manufacturing applications where we needed to improve bore finishes.

They sell these on Amazon and at $28-$30, they look like a reasonably priced solution. The only question is which one to buy. They list one for .223 diameter and one for .22 and .17 diameters.

Have you used this product for a 22lr? If so, which one?