The drain under my 1952 house is cast iron with (presumably) joints packed with okum and lead. Roots have intruded into one of these joints where a horizontal pipe section lying on top of the soil in the crawlspace joins a vertical tee (one side up to the roof, the other underground and out to the street). I believe the cast iron is still sound.

What is the best or most economical way to fix this problem which is causing frequent mainline stoppages?

I would think repacking the joint would not be too hard, provided there is an alternative to working molten lead into a horizontal joint in a confined space. The first plumber suggests cutting out the leaking tee and an adjacent tee (at least 4 cuts) then joining in new plastic with bands, but that sounds like a lot of expensive work.

Before I started replacing fittings that may still be of service try this. It's not the lead that makes a poured joint, It's the okum that swells and makes a water tight joint. The lead packs the okum in and retains the joint.
If you're quite sure that there are no cracks in the cast iron I would first recaulk the joint the roots are getting in, you don't have to repour or yarn in more okum. To control the roots RootX or Robics Foaming Root Killer that contain Dichlobrnic are two products you could try.
A less expensive way would be to call around to garden supply stores and ask for fine grain Copper Sulphate. Put a 1/2 pound in your toilet and flush it down. Repeat in 6 months.
Hope this helps and thank you for rating my reply. Tom

Thanks for the reply. What type of material can be used to recaulk the cast iron joint? Can the joint be recaulked on top of the old okum and lead, or should the old material be cleaned out of the joint first? Is caulking used by itself, or on top of new okum as a substitute for lead?

Hey Fiddler. Let me repeat my first post.
"If you're quite sure that there are no cracks in the cast iron I would first recaulk the joint the roots are getting in".     You don't have to repour lead or yarn in more okum.
You simply take a set of caulking irons and re caulk the joint using the original material. Recaulking the lead will pack the okum down tighter and close any cracks that might have opened to let roots in.  Hey! Get a old timey plumber, like me , that broke in on cast iron and lead and okum  joints.  If the cast iron's still good you won't have to replace anything with PCC.  Good luck, Tom