My GPA was 2.75, but to me, a GPA is just a gauge of someone's discipline and attitude. That's one reason why I am leaning towards joining the military. I believe it will challenge me and bring out the best in me.
I hate to burst your bubble, but applying for a commission is a screening process, unlike enlisting. Part of the mentality the board is going to use to screen you is: do you already demonstrate the discipline, motivation, and attitude to succeed as an Officer? By your logic (and I can't say I necessarily disagree), your GPA demonstrates that you lack those traits...so why would the Navy want to hire you (you'll get to explain this in 450 words on your application)?
If you want to enlist for personal development and to repay your loans, then go ahead. Bear in mind that you should try to pick a rating which will satisfy your professionally, or it will be a very long 4-6 years.
As for the LRP program, you are correct it is only available to enlisted Sailors. However, I encourage you to look at the base pay and BAH rates for an O-1 to O-3 with 0-5 years in service compared to an E-3-E-5 with similar TIS.