Before abandoning the old gasket, look for food quality silicone oil. It is in an aerosol can and is used to coat icemakers to ensure good release of cubes or whatever shape they make, crescents, drums, etc. It is more than just oil since the oil is the vehicle for the silicone. I bought it at an appliance parts store, but I am sure it should be available online. You might also find dry silicone in a spray can which is safe to use around food, indeed ice trays and cooking utensils can be sprayed with it, but you need to be very careful using it. Take it outside over an area covered with vegetation where you won't walk because the overspray and drifting particles make anything on which they land slicker than snot on a doorknob and underfoot that is very dangerous.
As to the gasket size, how many quart mason jars fit into your cooker? I realize it is probably not tall enough, but just to get an idea of the capacity. If it will not hold 7, it is of a smaller diameter than the Presto canners. I think that the 12 qt. Presto canners were stamped aluminum instead of cast so those gaskets would not work in your cover. There are Guardian Service groups online. I would Google that and ask about the gasket. You might find dealers who have them. If the cooker is indeed a 10 quart, I would Google ten quart Presto (or National or Guardian Service) pressure cooker gasket. You might find it that way.