Your question is confusing. First you mentioned using screws, then immediately jumped to toe-nailing. Could you be more specific about what you are really wanting to know?
I personally think 2-1/2" long screws are too short. If used perpendicular to the new sill plate, that means you're only getting 1" of grab in the studs. Worse yet if used in a diagonal orientation, from the opposite direction (like toe-nailing, but with screws), because the effective depth of penetration into the sill plate is reduced by the cosine of the penetration angle, less the normal distance from the interface to the point of entry. For example, 2.5" x cosine 45 degrees, minus 1" +/- = 0.77". Meaning just a bit more than 3/4" of effective penetration.