Sorry, but I don't have an account on lucid and don't fancy yet another source of spam emails. If I had seen the other thread earlier I could have suggested "dia", but a bit late now.
Anyway, some general observations on what you said...
You can have quite a few switches in a chain, something like 5 without issue which is probably more you are likely to get in a home environment. Note that is traversed not total, so if you have one central switch that feeds switches in other rooms in a star, then packets will only be crossing the room switch where they start, the central switch, and the switch in the destination room. That leaves wiggle room for a couple more switches badly daisy chained in without problems.
Adding more switches generally doesn't balance loads, the switch just finds what it thinks is the best path and sends everything down that one, if you are lucky. If you are unlucky, you get a loop which causes a network storm and everything grinds to a halt hopefully just for a short time until the switch disables one of the redundant connections.
If you want more throughput, you need link aggregation to turn 2x1GbE into a 2GbE connection which means paying for managed switches. That can work, but isn't ideal.
Transfer performance from a NAS can depend on a lot of things. I run PCs has home servers, and am currently migrating from an old FM2 quad core machine to one based on a Ryzen 3600. Both use a pair of hard drives for storage. Transferring a couple of VM images from the old server to the new one, the first one I used sftp from the new server to read the file from the old one, and got 70MB/sec transfer speed. Thinking that was a bit disappointing, the next one I logged into the old server and transmitted the file to the new one, getting 100MB/sec. Both big files, both same actual direction, but just down to whether I was pushing or pulling the data. Network protocols can be like that though, even though even my old FM2 Athlon is way more powerful than most consumer NAS boxes and the new server has an Intel network card, so play with your workflow.
OFC the smallest of those files was over 11 minutes to transfer, so the real answer is to upgrade to 10GbE or better. That means parting with money though, not something I'm good at