By “marinading it twice” I mean one marinade to get rid of the smell, another to actually season it. The second one is optional, up to you; you can reuse the liquid of the second marinade for some gravy, or to brush over the meat (never raw, though), but do not reuse the liquid of the first one.
Oh, also! Would you recommend both trimming/boning AND the lime brine?
It is not necessary but since you said that you’re noticing it around the fattier bits, I’d try it. (I never did it though - only the marinade.) Then, as you said, you can always readd some fat, in special lard would be good.