I would finish the quilt first. At that point, my biggest concern would be bleeding from the red thread.
It is quite possible that the red dye in the thread is not colorfast. What I would do to take care of this is wash the quilt with hot water and Synthrapol in the largest front-loading laundromat washing machine I could find. (A front-loader is easier on a quilt than a top-loader with central agitator. Domestic home front-loaders do not use enough water.) You want a large front-loader in order to have enough water to fully dilute any bleeds. Synthrapol will keep loose dye particles suspended in the water so they can be rinsed away instead of settling into the white fabric. Synthrapol needs hot water to work properly. If you don't want a lot of shrinkage, you might want to use a polyester batting or pre-shrink a cotton batting before quilting. Also, to minimize any shrinkage of the muslin, the quilting needs to be fairly close together (I wouldn't leave quilting lines more than 3" or 4" apart). This is because quilting fabric to the batting causes the batting to take control of shrinkage; the fabric cannot shrink more than the batting. If quilting lines are far apart, though, the fabric can lift away from the batting and shrink more on its own. If the muslin was not pre-washed, it could shrink a *lot*.
You could use a large top-loading machine if you can control the cycles in such a way that the quilt is never agitated by a central agitator. (If you have a top-loader that doesn't have a central agitator, this may be less of a concern, but you still may want to be able to control the cycles.) My biggest concern with a domestic top-loader would be whether or not it holds enough water to fully dilute any dye bleeds. You would want to keep the quilt continuously agitated so that there is no chance of bleeding thread remaining in contact with white fabric for more than a minute or so at a time.
Afterwards, I would treat with Retro Clean (
http://www.retroclean.com ) to get rid of the age spots. The reason I wouldn't use Retro Clean first is because you need to allow the quilt to soak -- which would allow bleeding thread to remain in contact with white fabric for a long period of time.
I don't think there is any safe way to prevent the thread from bleeding. This is why I would allow it to bleed if it is going to, but would take precautions that the bleeding dye particles do not stain the white fabric.
Edit: You may need to use the Synthrapol treatment more than once. Examine the damp quilt carefully. If you see any evidence of red bleeds into the white fabric, immediately run the quilt through again with Synthrapol and hot water. This will take errant dye particles out of the muslin, but the process may need to be repeated. (This is worst case scenario.)