Which of the two connectors, NAMELY and THAT IS, sounds more appropriate to insert in the following sentences:

Surely I already know what the contents of our contract are (NAMELY? THAT IS?): that I am to work for you for a period of 18 months, after which time you will release me with my debt to you cancelled.

This shows how little they were aware of the challenge facing them (NAMELY? THAT IS?)–
to reestablish prosperity and the rule of law.

Shareholders drew their own conclusions (NAMELY? THAT IS?): that it was time to sell out.

It would be helpful to consider what Dr. Slabbert said at the conference in Johannesburg (NAMELY? THAT IS?) , that the Department of National Health has the capacity to deal with major health problems.
'namely, that I am to work for you...'
'that is, to reestablish prosperity...'
'namely, that it was time...'
'namely, that the Department..'

Those are my feelings, and I don't see any rule emerging; just a style point that leads me to avoid juxtaposing two 'that's ('that is, that'), which seems rather awkward. If there is no following 'that', then I prefer 'that is', which is more expected, I think.

Otherwise, I would think that 'namely' tends (of course) to name, while 'that is' tends to explain.
The phrase "that is" is only used to explain. Its latin counter part i.e. (id est)

If your intention is to introduce examples or identify items in a list, use "namely." You could also use e.g. or (exempli gratia)