I'm a lot like you, Bob. If I'm riding my bike, I'm generally riding it to get somewhere. I can also understand how little things like this bother you (I'm still trying to figure out how I can ride to concerts).
I have pedals with SPD on one side, and regular platforms on the other. Maybe I'm just weird, but I've never found that I go noticably faster when clipped in. In fact, I probably only clip in about 50% of the time, because I find that the time and effort I use to flip the pedals the right way and clip in outweighs the advantage I get. And I'm almost always trying to go fast. So I'd have no problem wearing whatever I wanted to wear at the beach and just riding on the platforms. What kind of speed differences have you noticed?
About the butt, I'm apparently one of the rare (and lucky?) ones who does just fine without padded bike shorts. I'd have no problem doing 12.5 miles to the beach and back, and would probably just wear only the swimming trunks (in fact, I just bought a new pair of trunks specifically thinking that they might make good biking shorts since they're lightweight and quick-drying). Of course, that doesn't help you much!
As for the soreness, I think that most people get soreness anytime you change your seating configuration, but after a few rides your butt gets used to it. So maybe if you rode more without the bike shorts, the soreness would ease up (although that would be a disheartening and painful experiment if it turns out to be unsuccessful).
For the chafing, it's probably less likely that you'd get "acclimated" to that like you might with the soreness, but I wouldn't rule it out. Otherwise, I'd imagine it would mostly be an effect of a different seat, and the way your legs work around it. Why don't you try putting the seat from your comfort bike on your Volpe? For the record, I ride a Cannondale T800, which probably similar in positioning to your Volpe, except I got a Brooks B17 saddle for it, which I really like. I did get chafing down on the thigh just below the butt one day on a long ride, but that was when I DID decide to wear padded bike shorts for some reason. The next day I did another long ride, but switched back to my regular underwear and shorts, and the pain from the previous day's chafing actually got less and less as the day went on.
About the helmet, maybe you just shouldn't have gotten an expensive helmet. :-) But really, even if it is expensive, I can't imagine too many people would want to take a helmet. Wouldn't that be kinda like stealing a pocket protector? I commute with a Topeak trunk bag that slides onto my rear rack, and then slides off to become a nice shoulder bag which would probably hold beach gear well, and then you can just hook the helmet to one of the straps of the bag. Sometimes I do that, and sometimes I run my cable lock through a helmet vent.