I had this exact problem on both my 85 Trek 620 and my wife's 85 Trek 720, trying to put modern canti brakes on them. Front only, and the problem seems to be that the canti studs are too close by modern standards.
I fixed both of them by going to a smooth post type canti - on one bike, it was Tektro froglegs knockoffs and on the other VO grenouille brakes combined with judicious filing of the brake pad.
Dia Compe 960,
like these on ebay, came on the bike and worked on the 720, and if they could work there, they can work anywhere. On the 620, Shimano Deer Head M-700 cantis
like these on ebay came on the bike, again a very tough fit.