First of all, a couple of things:
one: if you want to maximise yours strength in the squat, you can't just front squat. Front squats will help your squat, but you still need to squat in some form quite a bit to get stronger at squatting. Box squats are often a favourite for those who don't want to just straight out squat.
two: what has competing got to do with a 350+ lbs squat? If you can squat, bench and deadlift 45+ lbs, you can compete as a total powerlifter.
Apart from that, simply based on my own experience if your deadlift goes up, your back is getting stronger. If your back gets stronger, it can take more load. This means you can squat more. How much your squat and DL feed off each other is going to depend on your individual characteristics. I'm lucky - my squat and DL have always been pretty close and they seem to feed off each other quite significantly. You may not be so lucky, but I still stand by the idea that a stronger DL = a stronger back = a stronger squat, EVEN IF that squat is far off the DL. If you pull sumo and squat wide, the carryover is going be probably as maximal as it gets.
Since you're tall, you may benefit from squatting with a wide(r) stance. IMO front squats won't be overly helpful to a wide squat BUT they will do a bunch to stop your quads lagging like mine did/do from wide squatting for a while. Just based on your front squat, I would estimate your squat is somewhere around the 300-320 lbs mark (I'm going on your 205x5 being around 80%, and your front squat max being about 80% of your squat because you train it so much. My front squat max is probably closer to 70-75% of my squat, but my front squat is a lot weaker than my squat). Anyway, that's around 100 lbs between your squat and DL.
All that rambling aside, just based on the numbers it looks to me like your back isn't so weak but you might just not be squatting the right way for your body. A video would be helpful to show where your weaknesses are in the squat.
Bottom line, of you don't want to compete, no need to squat. Ever. Front squats are a very, very good alternative and like Destrength pointed out, awesome assistance for DLs. If you want to get stronger at the squat, you're going to need to squat some. You can still front squat a bunch, but you'll need to squat too.
Hope that helps and makes sense.