Hi Miss Bubbles,
I don’t like to be the bearer of bad news but there really isn’t a reliable way to firm up or “fix” a mattress that has developed soft spots or has started to sag without first identifying and then removing and replacing the materials or components inside the mattress that are the cause of the problem. Basically you would be rebuilding the mattress using any of the materials or components inside the mattress that are still in good condition (which is unlikely after 20 years).
While the box spring may also be part of the problem if it has also developed soft spots or is sagging … it’s likely that the mattress itself is past it’s due date and needs to be replaced regardless of the support system underneath it.
All of the ideas you are suggesting really come down to using a firm non flexing support system under the mattress to replace your current box spring which as you mentioned will tend to firm up the deeper support of the mattress (a foundation won’t flex under the mattress like a box spring) but the only way to know whether this would end up being suitable for you to sleep on (at least for a while) or would firm up the mattress “enough” will be based on your own personal experience.
You could try sleeping on the mattress directly on the floor for a few days to see if this makes “enough” of a difference and if it does then you could purchase a foundation to use under your mattress to replace the box spring (a foundation would be similar to the floor since it would have limited to no flex). Most mattress stores will be able to sell you a foundation at a reasonable price. You could use the foundation directly on the floor or on a steel bedframe if you need some extra height.
It probably wouldn’t affect the airflow directly under the mattress enough to make a difference and it wouldn’t make any difference in terms of firmness compared to using your box spring (or a foundation) without a bedframe since it wouldn’t make the box spring or foundation any firmer than it already is … it would only add some additional height.
There are also some suggestions in post #4 here that may also be helpful … at least partially or temporarily,
Phoenix