Your transom shouldn't be soft anywhere. The solid laminate the manufacture tells you is there may have had an incorrect hardener to resin ratio and it's not completely kicked off (and likely will not) It may be a sandwich type of deal where a resin was poured in-between the inner and outer skins, this may have sheared or otherwise delaminated. Or simply the manufacture may have been mistaken and there is plywood in there (possibly a repair) and the bedding broke down letting in water and now it's starting to rot.
Whatever the reasons, you need to get some good material back in those areas that seem effected. There's no real short cut to do it right, so get out the grinder and gain access to the areas. You find there is more rot then you thought (good thing you opened her up) chip, grind, chew and remove all traces of delaminated or rotted material. Do this on the inner skin if you can as you'll save the outer skin and it'll look like nothing ever was wrong from the outside. Grind back the edges of the good glass to a feather edge, say about 4" wide (the taper ground into the glass should be this wide) this provides you with a large surface to bond the repair to. Now you have a few choices for filling the area(s) plywood, cloth/roving/mat, solid resin or application specific products.
If it seems to be just around the holes (it never is, it's always worse once you get to see where the damage is) you can try the "pour in the hole" epoxy products available. My experience has been if the transom is soft anywhere, the rot is wide spread, not just around the holes, but traveling down (the gravity thing) to the bottom of the transom, where water has been pooling and even more localized rotting. I've seen people pour quarts of epoxy into holes that never seemed to stop absorbing more epoxy. What happens is the epoxy runs through the rot created voids and ends up at the bottom of the transom or worse out of the transom and into the bottom of the boat.
If using a product like SeaCast then follow the instructions, but the jury is still out on that stuff and the folks who run the place have plenty of advertising hype and testimonials from their fans, but haven't gotten off the product specifications for me yet. I'm not mean, but I'd like to know the shear, compression, tension, flexural strengths, elongation percentage and water absorption rate before I start pouring the stuff into customer's boats.
In any case, the repair is pretty straight forward glass work after the rot or delaminating is gone. Epoxy is stronger and more water resilient then polyester. It also sticks a bunch better to plywood then poly. If using plywood for the repair, you must use epoxy if you expect a long lived repair.