Can I install rigid insulation to the underside of an existing ceiling?
It would be a very expensive and cumbersome way to go, with new sheetrock, new paint, etc., not to mention additional load on an old ceiling.Is this possible to save money? Of course it is, here are some work to do first.
Assuming that your attic was vented somehow - most were back then.Make sure those vents work. If the soffit vents (the ones at the edge of the roof) and/or gable end vents are closed up with dust/debris then you have an oven for an attic. If the hot air is allowed to be vented out of the attic (perhaps through the gable ends --- they did not use ridge vents back then to my knowledge) naturally then that is a good thing. But note even if the gable vents are open, if the soffit vents are closed then the natural “stack effect” will not work (heat rises, to be replaced by air being sucked into the attic through the soffit vents). This should not cost anything other than time and sweat.
You can purchase insulation with a radiant barrier (this is the shiny foil like side). The radiant barrier will actually do a very good job at preventing radiant energy from entering your attic. Apply this insulation, reflective foil side facing the interior of the attic---not against the underside or the roof--- between your roof rafters and also on the gable ends between the gable end studs. This is another low cost operation. When you are done you should see a shiny surface looking back at you from the underside of the roof and each side of the attic.
If you care to keep going,clean out all the old insulation---much of it was probably clogging up the soffit vents. Be prepared to find lots of dead things in the insulation ---it’s not pretty. A fairly cheap way to go is to buy Landy insulation.
The above things should be done in the early morning --- like start at 4am and work until 10am or 11am if you can stand the heat. This is the cheap but fairly effective way to go. You want the warm air to be able to pass through and out of your attic through the soffit and gable venting, and the radiant barrier will help to reduce the radiant energy inside the attic and the cellulose will help to insulate from the house below.