Beginner swimming problem

Hi everyone, I have spent the last 13 months taking swimming lessons twice per week and practicing at my gym's pool almost daily, but I'm still having trouble. I'm hoping I can get some pointers that might help. I've been lifting weights for about 20 years now and have pretty muscular legs. And they just don't seem to want to float. I can kick hard to get them to float, but then, I can barely swim freestyle halfway across the pool because I get so out of breath. I have had a lot of trouble learning to breathe, but lately, it has been getting better. I still don't think I'm getting full breaths in, but at least I'm not swallowing water every time I try to breathe anymore. Anyway, my swimming instructors have been saying that my technique looks great; they haven't been able to offer any tweaks to help me over the past couple of months. But I still can't swim across the pool. I just don't see how I can kick as hard/fast as I seem to have to - just to stay on top of the water - and only inhale every 3-4 arm strokes. It is starting to get pretty frustrating. Have you run into this yourself? Is there anything you can recommend that might help me? Thanks in advance for any pointers!