-- some quick and dirty math suggests that your included leade angle is roughly 1 degree, give or take, depending on how I interpret what Jesse said. 1 degree is pretty common on benchrest rifles these days, and it's what I'm using for my 30-06 project.
-- the bottom half of the bullet will be supported by the case neck
-- the front band can be seated out until it kisses the rifling
-- you can spec the nose so that it kisses the rifling, too. The nose does not have to be 0.349", you can make the nose 0.353" or whatever you anticipate the leade diameter will be at the tip of the bore riding section. It doesn't have to be perfect since the front band is already centering the bullet and any nose contact is just a bonus. Once the bullet starts moving, the nose will engage the rifling.
-- here's a suggested tentative design, just to show what is possible. Note how I "cheated" by making the front band 0.351." That increases the bore riding length from 0.300" to 0.350". PLUS
there is a lube groove between the 0.351" front band and the 0.309" band below it, so when you add the length of the lube groove, the bore riding section is over 0.400" long (you can leave that particular lube groove empty so you don't have exposed lube). Seat it out until the 0.309" band kisses the rifling, and that should put the tip of the 0.351" bore rider darned close to the rifling. Maybe it will engrave, or maybe not, subject to as-cast tolerances, chamber tolerances, chamber erosion, etc. -- but it'll be darned close to the rifling, and it'll engrave as soon as the bullet starts moving.