MartyD,
I grew up on Long Island, not too far from where you are. I know the water table there and it's soft enough for filling a pool with. There is no reason why you can not use a mixed chlorine strategy .... although NEVER physically mix your chlorine sources
If I were you, I would use an inline puck feeder to deliver trichlor derived chlorine to the pool and set it on it's lowest possible dispensing rate. Then, for daily chlorination, I would add whatever amount of cal-hypo is needed to keep FC levels steady. You would broadcast the cal-hypo powder around the pool and brush vigorously to ensure no granules sit on the liner. Every 10ppm FC added by trichlor adds an additional 6ppm CYA to the pool and every 10ppm FC added by cal-hypo will add roughly 6ppm to your CH. If you keep a close eye on your CYA through out the swim season, you can stop using trichlor as soon as you get to 60ppm (even 70ppm is not so bad). Then you would simply switch to exclusively using cal-hypo for the remainder of the season. You are not going to build up enough CH to cause a problem but you will need to aggressively manage your post-season water levels to ensure that you are maximizing the amount of fresh water exchange you can put into your pool (seasonal rains and winter snow melt).
The one caveat with cal-hypo is that it tends to raise pH strongly and so you are going to want to keep your pH and TA on the lower side so that temporary cloudiness is mitigated as much as possible. Usually with cal-hypo you'll find that the water gets a little dull right after you add it from calcium scaling but that should go away rapidly with filtering and time. It's simply due to the more caustic nature of cal-hypo powder.