The string deal will work for the rear stays but to check the steering head tube you'll need to get a little more imaginative. I'm thinking two long builder's levels shimed so they sit level. Lay the seat tube on one using some packing with matching lift to set the seat tube parallel to the first level. Then use the second level at the head tube and measure to the lips on each end. They should match to within a fairly small tolerance. Flip it over and check again.

It would be even better if you could arrange a tube that sits locked into the bearings so you're checking the true steering axis but that would require some fancy playing around to make up jigging device to do the job.

For the head angle you'll want the frame geometry. Using a pendulum angle finder from a hardware store set the frame up so the seat tube angle matches the spec table for your frame. Then measure the head tube.

If the measurements match closely then you're fine. For the first test you're looking for a difference bigger than something like a 1/64 inch (.015 inches). For the angle if you're within 2 degrees you should be fine since those angle finders are just so-so to read from the small scale.