NER Regatta Braid

Are you meaning an end for end splice? When you said reeving splice I thought you were just wanting a loop that you could tie a tag line on to. Hmmm, as far as I know you are going to get an increased thickness no matter which method you use (though hopefully more of a splicing guru than I can help you there) but with a good tapered 12 strand it's usually not that thick. Perhaps your sheet blocks are undersized. What hardware are you using and what size line is it? Hopefully brion or one of the other splicing wizards will join in here.