The discussion I was remembering is from
this thread in the old forums. Looks like people got level 10 by day 7 (version 1.3, I believe, but that doesn't really matter, no exploits were used). But it's worth noting that they were spending 100% of their time and money on fishing, which I don't think is a good idea - in particular, I don't think it's worth spending 7.5k on the iridium rod in the first week of spring, YMMV.
How many perfects do you get (I assume you're a pretty good fisher, if you're doing it that much and you're catching catfish week 1) and how early do you buy the fiberglass rod? IMO if you're going for levelling up fishing, as soon as Willy's opens on the 2nd you should be getting the training rod for easier perfects, and then ideally you hit level 2 fishing and buy the fiberglass rod before Willy's closes on the 2nd. (Money for the rod and bait comes from running around the map D1 and selling fiber and forage, plus the fish caught D2.) I personally like to stay by the ocean on the 2nd, at least until 5 pm, it seems to work better than running up to the lake and running back down to buy the rod.
Fiberglass rod doubles your xp rate, which means you level up faster, which speeds up bite times for faster xp, and so on. Definitely worth it to get it as early as possible. After 5pm, not sure if it's better to stay by the ocean and fish, or go up to the lake. IIRC, the ocean is better xp, but the lake is better money. I did this before 1.5 came out (staying at the ocean all day) and after 5 tries or so I managed to get level 4 by the end of the day. (For me, getting enough money was a bigger issue than getting enough xp). If you can get the rod and the bait by 5pm, it should be easy enough to at least get well into fishing level 3.
Day 3 I went to the river. I barely got level 5, but I was spending some time running around because I wanted to also buy copper from Clint for an early pickaxe upgrade. (And then I realized I didn't have enough time/money for the actual upgrade... oh well). Also I apparently suck at catching catfish at low levels. Anyways that's where I stopped because 1.5 came out, but I was only 227 xp away from level 6, and with fishing at the lake I bet I could have gotten to level 7 on day 4, and then level 8 on day 5, or day 6 at worst. Even if you don't get fiberglass until the morning of day 3, that puts you less than a day behind me, so what I said above about level 8 by day 7 is probably still doable.
tl;dr buy the fiberglass rod early! And work on perfect catches, but it doesn't sound like that should be a problem.