I think if you are going to be using Free Software as an accessibility tool for uni, then you need to sort out exactly what software you are going to use now, before you start and things get busy. Try it out, try doing some writing with it, etc. Is it effective? Can you live with it? Does it have all the features you need? Does it integrate well with any specialist software you might need to use?
Also bear in mind that you might be able to use the proprietary accessibility software on university PCs, lessening the importance of running it on your own laptop, but there’s definitely an advantage in not being reliant on busy computer rooms.
Personally I would try to think of the DSA laptop/software as part of the course, like something provided by an employer, rather than a personal purchase. Yes, technically you might own it once it’s given to you, but that’s just a quirk of the system. This is the mechanism by which the education system is providing assistance with your disability. The choice you have is more along the lines of “take assistance” versus “take no assistance”, rather than “use non-Free software” versus “use Free software”. If they were saying “you’re on your own; we’re not helping you with this, sort it out yourself”, or if they were offering just the software rather than a complete solution including a laptop, then it would be different.
Yes, it would be better if they used Free Software, but you boycotting the disability support isn’t going to change that. It’s just going to potentially disadvantage you academically, if other dyspraxic/dyslexic students have more effective software aids. (Sadly.) Better to find allies and campaign for change if this is an issue that’s important to you.
Rather than dual booting, consider running Windows in a VM. It’s so much more convenient. With hardware virtualisation and enough RAM, the performance is a non-issue if you’re not gaming. The only issue I can see might be if you need to use unusual peripherals that require Windows drivers. USB pass-through can be a bit hit-or-miss. A USB headset or microphone should be OK though; just let Linux deal with the USB bit and pass it through to the VM using its virtual sound card. (Make sure it’s not muted or set to the wrong input on the host!)
Dual booting is useful if you’re gaming, or if you want to make use of the OEM copy of Windows that came with your computer, but otherwise a VM is the way to go, IMO. I needed to use some Windows software for my course and I did it all in VirtualBox.
With dual booting you end up stuck in Windows and installing all kinds of Windows programs and utilities to enable you to do the other things you needed to do, just because one thing you were doing needed Windows. With a VM you can just install the bare minimum in Windows and do the rest in the host OS.