Barber's Adagio for Strings isn't what this piece reminds me of most. In fact, with the idea of minimalism that Antiatonality mentioned, it would more likely fall in the line of works such as Gorecki's Symphony No. 3. John Adam's is often considered or lumped together with minimalism composers. However, he treats minimalism as a technique, not a style. I would also consider him too eclectic to be put in the same category as early Philip Glass or other purely minimalistic composers.
If you listen to Gorecki's symphony and listen carefully in the first movement, he does a VERY long figure in this same manner, starting in the DB and rising to a full string orchestra. So what AntiA suggested might not be what you want to do at all. What he suggested was in the same line as Barber and his piece. However, Gorecki does a splendid job with the low register beginning.
The problem of orchestration does come into question when you want to create climaxes with a piece like this. I think the solution that Antiatonality provided can work well. Dropping some of the voices out and bringing them back in can make the texture and sound become very large and opqaue again very quickly. Done in the right way can amplify the feel or size of the sound to the audience and can create the right kind of idea of sound. Also if you explor the timbres of the string instruments in this way, a suddden change in the timbre can also do the trick. Barber does this in adagio. Or if the whole chorus of strings is put into a certain register, that is also a good idea. Explore the scores of both works, the Adagio and Gorecki's 3rd.
Also a variation in the rhythym would be a very good idea, possibly augmenting or diminishing the theme so the harmony and proportions are technically the same....
I just looked at the score as well-- You
do have some problems with the orchestration in terms of register. Look at more string works, including some very standard string orchestra works to see how they do this.
And you WILL want to think of a way to set up the harmony better.
Good luck.
P.S. I also like the idea of more percussion... maybe... It depends on how you would use it. I'd suggest only sustainable pitched percussion instruments. A vibraphone maybe?