Our property has a creek that is mostly filled with sandy sediment. It is amazing how much a decent rainstorm will re-distribute that sand within the creek terraces.
If you could create a wide, flat area beyond your pond basin for the sediments to fall out of the water flow, then the creek would do some of the sediment removal work for you.
The spring flows at those low rates will not create a sufficient flow velocity to move the sand.
However, your springs are enough to mostly keep your pond full - even if you dig it deeper! Based on your dimensions, your pond is about 0.69 surface acres. If you lost 1/4" of water per day due to evaporation, that would be 4,684 gallons/day. Your springs at 2 GPM supply 2,880 gallons/day. Add in some additional rainfall, and the pond should be fine.
Are you sure your spring flows are only 2 GPM, that would just be a tiny trickle going through two 24" culverts?
Deepening the pond will NOT increase the evaporative water losses. However, it may increase your seepage losses - since your pond will not be perfectly sealed and the seepage water losses are dependent on the depth (hydrostatic pressure) of the pond. IF you are going to spend the money to rebuild the pond, then I think deepening it at the same time would give you a MUCH nicer pond for only a fair bit more of costs.
I hope that helps answer a few more questions. (If not, keep asking!)
