Go to an 80# leader, leave $200 worth of braid on the bottom every year
Your leader MUST break before the braid. Otherwise it costs you money and leaves line balls out there for other Canal guys to lose tackle on.
40# leader with 65# PP. The difference between 50 and 65 PP is a lot. Before braid came along, 30-40# mono landed many large bass in the Canal. Guys didn't know what a "shock leader" was. They tied direct with 30 or 40 pound mono.
I'm not familiar with your rod. "Heavy" doesn't mean much in the abstract. You need a stick that can cast 6-10 oz easily to turn a fish. Otherwise, you should climb the bank to the road and walk with the fish. Standing there and letting her run is going to end up the same way most of the time--with a lost fish. You either have to break the fish, giving no quarter, or climb and walk. Change the angle--it really helps. So does getting up to the road. That also changes the angle.
I'd spool up that 704 with 30# Fireline, and run a 50# mono leader. And I'd look for a no BS rod. It would be worth the coin to invest in one dedicated custom Canal jigging stick. Have it built on either a Lami 121 3M (glass) or a Batson SU 1209. Those are the two best rods I know of when it comes to down and dirty weapons to break a fish's will. They'll run low to mid $200 range--money well spent.
One more thing---your biggest mistake, it seems, was letting that fish get up a head of steam. As I read your post, I can't help but think that your drag was set way too loose for starters. I fish about 12 pounds of drag, all the time. You have to take a wrap around your hand, almost, to pull line off my Saltiga. You'd still be surprised at how easily 35-40 pound fish pull line off, even at that setting--but they don't do it for nearly as long