All this talk about losing strength during the season is bull. It has never happened to me. You just have to train smart, and eat more. You may lose something at first, because you are not accustomed to the training and games. But once you adapt, you will at least maintain, if you are smart. Thinking you will lose strength in-season is mentally defeating yourself before you start. Virtually all the boys I am coaching now are actually gaining strength in-season.
One thing I think is worth mentioning is to train your legs the day after playing. You will be a little sore, but you will have fresh legs for trainings and your next game, which is more important.
I love strength training both as a means to improve my rugby and that of my players, and as a thing in itself. But don't get obsessed with it directly co-relating to rugby performance, because it is only one of many factors which influence how well you play. Aerobic and anaerobic fitness are obvious, but really, skill and rugby knowledge are paramount. Especially, players in North America start the game later in life, and usually have good physical attributes, but are rubbish at basics like tackling properly, rucking, passing, kicking, etc. They don't know the rules well enough and don't run good lines or anticipate, read defences, etc.
Get yourself some videos and books, and learn, because no doubt you are big and strong, going by pics I have seen of you, you will do okay physically. Slightly cut back your lifting volume but not your poundages, and get fit. You will then be on your way to be a good player.