Law 24 (No ball) prohibits underarm bowling except by special arrangement, as your findings indicate. If the captains were to agree to underarm bowling, I don't see how it could be considered deceptive, since it has been specifically highlighted and therefore is unlikely to cause any surprise, especially since you would have to inform the umpire and batsman when you are going to do so.
It would not be a sustainable long-term strategy as I would not think captains likely to agree to underarm bowling (it was used in an infamous incident in a 1981 one-day match between Australia and New Zealand). Coincidentally, I was playing cricket yesterday and one (new) player did end up bowling underarm; it was a social match and we did not object, but in future it will be necessary for him to learn to bowl overarm.
Finally, without knowing the intricacies of fastpitch softball, I would be doubtful that underarm bowling in cricket would do anything other than provide an easy hit to the batsman. The renowned England captain Mike Brearley would occasionally bowl underarm, but he was primarily a batsman, not a bowler; his was an attempt to try something new to unsettle the batsman. It didn't work: as far as I know, he never took a wicket with such an action!