I'm pretty sure you already know the answer. Invest in the filter. It'll be the best $100-$200 you've spent in the hobby. You'll also be able to use it outside the hobby, which isn't something people usually consider. I'd say it's an even split for me and I have a ton of tanks.Would this be fine for breeding caridina shrimp or should I invest in a small RO/DI unit?
You can chase parameters if you want but you'll never really get them where you want them and won't likely be able to maintain much in terms of stability. Meaning the environment won't be ideal for the shrimp you want to keep. Or you can get a reverse osmosis system, use a quality buffering substrate (don't use inert, it's a waste of your time and effort with shrimp like this) and add your own mineral salts. With this second option, you'll encounter fewer problems and will have less of a headache. More of a set it and forget it option.
That said, I wouldn't try to keep fish with them - I'd have a separate shrimp tank. Especially if you're trying to breed shrimp. The two don't really go hand-in-hand. It's a bad idea - especially with expensive, sensitive shrimp.
Also note that you'll likely encounter plenty of people in the hobby who frown upon hybridization of shrimp. I'm one of them and believe it's a terrible practice akin to what's occurred in the dart frog hobby in the past. But to each their own.