Though I can appreciate your wanting to keep the cost to a minimum, the cost is the cost, and someone has to pay it if an aircraft is to be airborne. Thus either you pay the cost, or you do something for someone else, so they are happy to pay it for you.
My early days of flying were many hours of doing "joe jobs" around the airport, in return for the odd flight. Owners of aircraft are often quite inclined to take you flying, if you have just spent the day scrubbing their aircraft to a glistening sparkle (particularly the belly). That is not as easy as it used to be though, simply because of airport security. "Keeners"' just can't hang around the ranp, as they did in my day.
Added to that, any operation flying Diamonds for training is likely only interested in dollar payment for the use of there aircraft. Some out of the way school, with older aircraft, where things are more casual offers a better chance of trading for some flying, but is by no means certain.
Your best way to economize is to pay for the flying you need to do, and prevent wasted time in the air, by being extremely well prepared for each lesson before you go, with a lot of self study, and rehersal. Though I'm not keen on computer flight simulators, they do have some merit as procedure trainers.
Remind yourself that if it is your intention to present yourself to a potential employer for a pilot job, or to an insurance company to be covered to fly someone's plane, you don't want to be presenting yourself as a person who got where they are by doing only the bare minimum.
Good luck....