Not sure why you would need to do both. If linings already drilled for rivets, then if properly installed they will work fine. Bonding is done with adhesive and heat and pressure which obviously works great also. You'll get more braking events with the bonding than with riveting since you don't have any rivet heads to run into and potentially score your drum. But most likely not an issue on a collector car?
i have a 1924 star and just had my rear brakes done i had mine riveted by industrial brake and clutch in morganville,nj they do 1 day turn around they did great job , i supplied lining or they have linings cost was 85.00 a shoe with my linings with there linings 125.00 a shoe