$600 isn't going to buy you a very lightweight bike, in fact, spending that kind of money will either get you a bike as heavy as what you now have or heavier. That brand you have is a nice brand of bike, and it's custom-made, why you would want to replace it is beyond me. If you feel it fits funny then go get a fitter to make it work for you. But since that bike was custom made they took all the measurements you gave them and made it to fit you, so it should be spot on, so something as simple as changing the stem length, or moving the saddle forwards or backward or higher or lower might make it feel better. So get fitted, spend some of that $600 on that instead of another bike.
Weight is not a big deal when it comes to bike performance. Instead, focus on factors like tire choice and frame construction. $600 or less can buy you a nice vintage touring bike that was lightly used, but you'll have to research to find out what the best ones were. but something like a Schwinn Voyageur or Voyageur SP around the mid-80s were fantastic touring bikes.
The bike you have now is fine, what you should consider doing is looking into a new set of wheels and tires, and possibly upgrading a component or two...OR, keep saving money and just buy a pair of nice lightweight tires that roll fast, plus a pair of 65-gram butyl tubes, or latex tubes if you're ok with using those. Then save up money for a period of time till you get to around $2,000 or so saved, but even that amount will not surpass what you bought, but you could find a decent touring bike.
I'm partial towards Vittoria tires, you would be surprised as to how well a pair of Corsa series of tires will feel on your bike, but don't buy them unless they're on sale, I see Vittoria tires all the time on sale for about 40 to 50 percent off, that's when I buy them. September and October is when road tires go on sale and closeout sales, but you have to be fast because they have limited stock, and when they're gone, they're gone. For example, last year I bought 2 pairs of Vittoria Open Pave CG III for $80 total, that's $20 each, they sold for $80 each, but I got a huge closeout sale and was lucky I found them when I did. The tire that replaced the Open Pave that I got is the Corsa Pro Tubeless Ready, which means since it is tubeless it will be a pain to put on, but since it uses 320tpi of cotton and a Kevlar belt for flat protection it rides darn near like a tubular tire especially when used with a latex tube.
I also wouldn't upgrade components unless one broke, you know the old saying, if it ain't broke don't fix it!
There is another option, you can change the bike you have for medium or lighter touring, they have special panniers that fit on bikes without bosses for panners, but it will take some research. Or you can buy a lightweight pull-behind trailer, again research will be needed to choose the right one for you.
Keep in mind that touring with a load is difficult, and you said you're a casual rider, you will need to change that to being an everyday rider and riding 40 to 60 miles a day because remember, when touring you're carrying an extra 60 pounds or so of gear, food, and water, and doing so every day averaging 40 to 60 miles a day, and that weight becomes a burden if you're not prepared for it. Or you could also do credit card touring where you don't take much with you, some basics, some clothes, sleep in motels and eating in restaurants. Research the different ways to tour. Research camping gear too. I had to do all of that myself when I decided to do loaded touring, even after a lot of research I had to make a few minor changes but thankfully it didn't cost much. And always start out with the least amount of gear you think you need, you can always add something later, but if you start out with too much then you spent money on stuff you didn't need, and then either throw it out on a tour or send it home, most new to any type of backpacking or bike packing overbuy.
