Are you able to keep your current job and fly on the side with either a regional or a small cargo operator???
Very doubtful.
Check your employee handbook
very carefully, there may be wording in there about being employed by another air carrier while employed by Delta. Some companies say an absolute NO to be employed by any other air carrier (in any position), and you also have the scheduling issues. Do you really think it would be possible to sit reserve as a new-hire regional F/O, and still "be" a Delta F/A? The scheduling would be berserk! Sure, you'd have swaps and drops, but I would think the stress of juggling the schedules would be incredible.
Also, if its that you don't want to leave and lose your "hire date" at Delta, keep in mind it's going to take
years to gain enough hours to meet the min qualifications to submit a pilot app at Delta. You'll start at the bottom of the Delta Pilot's senority list regardless of prior DL employment, so you won't get a better schedule or pay for being a current (or former) DL employee. You'll still be a "new hire"
pilot, even if you've been with the company for 10 years.
Many years ago I tried to start my pilot training while I was a F/A at Eagle. The scheduling was murder. I was working 4 days a week, but it seemed like my days off were
never right for flight training! The weather sucked, or my CFI's schedule and mine didn't match up, it just wasn't working. I went over to mainline AA, and put my flying on hold, and I didn't end up getting my PPL until I got furloughed from AA in 2001.
Personally, I recommend taking a few lessons while you're still a F/A, make sure it's something you REALLY want to do, and once you made that decision then quit and go all out and get it done. If you can swap/drop trips so you don't have to work much, you could probably keep working and do it, but if I had it to do all over again I'd put in for a leave at Eagle and just go get it done.
Good luck to you