Thanks for the background info. While I understand your predicament, I encourage you to choose the best solution, not just try to "save" one that may be inappropriate. If something goes wrong during construction or service life, people will be coming after you and they won't care about why H-piles seemed convenient at the time. Also, I'd recommend you involve an experienced geotech in the final design decisions. My instinct tells me driven piles are not likely the best design solution but I don't know enough about the project to say for sure.
Not sure what pile driving formulas you're using. Most I've seen are to correlate hammer blows to load capacity.....not to evaluate whether you can drive the pile through the material in the first place. While the wave equation can correlate the hammer blows to the load capacity, it can also perform a "drivability" analysis to see if you can install the pile to the depths required. It looks at the specific pile hammer, cushion type, pile dimensions, etc to figure out the stresses in the pile, etc. Basically, yes I would recommend this if you really are planning on using driven piles. If the contractor goes out there and can't drive the piles to the depths required, everyone is gonna have major problems. Remember though, with your situation, you are not going to be able to rely on blows as an indicator of capacity during installation. Plus, it will be difficult to perform a load test that will assure you meet your assumed capacity. (Since the upper soils will provide resistance during installation but can't be counted on for long term load support).
NSF and dragload are basically the same thing (NSF mechanism causes a downdrag load on the piles). You should design for the worst case of dead+live load and dead+NSF load. Since the live load is short term, the settling soils that are causing the NSF will provide a resistance to settlement from the live load (i.e. they are weighing down the pile but at the same time they are providing an equal capacity to resist the very short term live load).
About the "dragload must not be included in consideration of the geotechnical capacity", this is for evaluation of a plunging failure, not settlement. For example, say the soil is going to settle 2" and therefore cause NSF load. Ok, so then once the pile settles 2", there is no more NSF load. So although the pile has moved 2" (which is probably too much settlement), it has not experienced a plunging failure. Because the settlement can alleviate the NSF load (unlike with a structural load), NSF is not considered in plunging evaluation.
I'd question designing the H-piles based on end bearing (I can't believe you'll get a large capacity out of the end bearing in sand). Sometimes on rock or very dense materials this applies but not in most soils since the cross sectional area is small. Usually in soils they're designed for skin friction.