i find the reverse grip close grip bench press doesnt aggravate the tri insertions. Also the seated dip machine alows you to play with hand/palm placement while leaning forward or backward at different angles to find your "pain free" spot. I also do rope press downs with a lighter weight for 15-20 reps for at least 5 sets. Palms facing in feels ok. Once warmed up I can move to wider grip straight bar press downs.
In contrast, close grip, regular grip bench press is also awsome for tri's but really a huge no-no for me. (pain!) I would also love to be able to do regular dips. But all the ancilliary muscle and tendon support that is needed to balance/stabilize the entire body just murders my tri insertions which pisses me off cause I have never ever had as huge of a pump in my tri's as when I did "real" dips.