Welcome to quirks of NSX ownership!
I have a 2000 with the later design dual mass flywheel / single plate clutch so my experience may not be exactly the same as yours; but, I have test driven a 1991 dual plate and I don't recall a lot of difference in clutch feel. For what it is worth, I embarrassingly stalled both the 1991 and my 2000 when first taking them for test drives because of the rapid clutch engagement. I don't think the issue is the clutch but the linkage design of the clutch pedal / master cylinder / slave / clutch fork. The NSX (and a lot of Honda products) seem to have the linkage designed to provide for very fast disengagement of the clutch and the leverage in the mechanism provides for a narrow engagement point. The disengagement of the clutch occurs during the top part of the pedal stroke and the flip side of this is that engagement of the clutch does not occur until the clutch pedal is approaching the high point of its travel (all relatively speaking of course). This makes for quick release of the clutch and fast shifting when you are moving; however, as you have discovered not so much fun in stop and go traffic and stressful if you have to do a start going up a hill.
I think some owners smoothen out the start by revving the engine fairly high and then sliding the clutch out. That does make for a smoother start (or at least avoids the embarrassing stall); but, as you allude to can result in fairly short clutch life. Search Prime and you can find owners complaining about 25,000 mile clutch replacement intervals. My current style of clutch operation is a version of your third bullet. I release the clutch pedal up and as the clutch starts to engage I apply some throttle. Do it smoothly and there will be is no over revving, slipping and lurching. Of course, for this to work you have to train your foot to know where the start of the engagement point is and that just requires some practise. Go to an empty parking lot and just practise doing some starts, releasing the clutch pedal and listening for the engine RPM starting to drop and then gradually applying some throttle. A little practise will smoothen things out. However, even after 10 years of ownership, on occasion I still release the pedal too quickly, hear the RPMs die, press the clutch in to recover, see the RPMs increase rapidly, release the clutch too quickly and lurch away from a stop.
That said, clutch operation can be complicated by incorrect adjustment of the pedal. There has to be some free play in the clutch pedal as set out in the factory service manual (you can find links to free .pdf versions of the FSM on Prime). If there is no free play you will have faster release of the clutch and potentially a worn release bearing and in worst case a glazed clutch facing. Check your free play to make sure that it is correct. If the car has an aftermarket performance clutch these typically come with very narrow engagement points making for more of an on/off experience and a pain to drive. If a previous owner replaced the flywheel with a lighter flywheel this will result in the RPMs dropping faster during initial engagement making a standing start more difficult.
I don't think you will ever be able to do a standing start without applying some throttle as you describe in your 240 Z. The final gearing and lack of flywheel inertia conspire against that. If the problem really bothers you you could consider installing a short final drive ratio which should make starts easier; but, be prepared to live with more engine noise on the highway.
