Yep. The absolute best way to keep from seeing the rubber tube is to not use a rubber tube at all.
Your short draw is not setting you up for severe string angle. If anything, it's just the opposite. String angle is determined by draw length and bow length. The lower that ratio, the more acute the string angle. Because of my draw length/bow length ratio (31 3/4" draw, bow length 36" for a 1:1.13 ratio), and the distance from my nock point to the peep location, my peep winds up about 8" out in front of my eye at full draw. I went to a G5 Meta peep with a quarter inch hole. It's very good at presenting you with a round hole due to it's curved inner surface.
Now, if I can see through a round 1/4" hole that's 8" in front of my face with my old bifocals beset eyeballs [8D] surely you don't need a peep that's bigger than that.
Basic rule of thumb. Use the smallest diameter peep that allows you to see through it clearly, under the worst lighting conditions you expect to face.