Looking for router that can handle 3TB exFAT / HFS+ external HDD

Question

I recently bought a WD My Passport Ultra 3TB external HDD. It's performing beautifully and blazing fast, zero complaints there. However I did find out that my aging router (TP-Link's TL-WDR4300) doesn't support GPT-formatted external drives. Formatting the drive to use MBR would result in the router only seeing 2 out of the 3 TB of storage, which is a no-go.

So I made a bucket list of my requirements for a new router, but so far have been unsuccessful in finding a device that fits them all. I suspect even if I find it, it'll be $300+ but I can swallow that -- it's not like you buy a router every few months.

My requirements:

• Gigabit WAN (future-proofing, you know).
• Gigabit LAN, 4 ports.
• 2 or more USB ports. At least one has to be USB 3.0 because that's where I'll put my external HDD.
• High availability / resilience to overloading (not against DoS / DDoS however; I don't think there are routers who can withstand a focused attack anyway so that's out of my wish list). My WDR4300 "clogs" if I seed my Linux / misc OSS disk image torrents for an hour or so; it stops serving internet connectivity to everything at home even if I stop my torrent program. I limited the software's maximum allowed connections to 150 but that only makes the seeding period little longer -- around 4h at most, then the same thing happens. Only a restart of the router helps.
• I want the external HDD formatted in a file system that will allow me to use it everywhere I wish: on my Win10 PC, on my Macbook, and optionally on an old Linux / FreeBSD laptop. Plus, I want it recognized by the router of course. In a nutshell, I want the HDD to normally reside at home and be usable by the entire family through the router but I also want to be able to unhook it and carry it with me if the need calls for it. To that end, I was unable to find a router that can use a GPT-formatted exFAT external HDD. I am not against formatting it to HFS+ and use it on my PC through Paragon's HFS+ paid software, if that is what it takes to find a compliant router.
• RJ-45 compliant. I don't care about optics or SIM slots.
• Print server. That however might not be critical because TP-Link already has a program that I installed on my Windows 10 PC and it almost immediately found my printer. I'm guessing the lack of print server can be alleviated with similar means on other brands, but do correct me if I am wrong.

Nice to have but not a deal breaker:

• 5Ghz network.
• OpenWRT / DD-WRT / Tomato compatibility. Not very fussed about that however; I tried using DD-WRT on my WDR4300 but after being unable to set up a guest network even after following the officially documented ways of doing it and even though I repeated the process probably 5 times (accompanied by restarts), I finally gave up and was left scratching my head on why do the open-source tools make it so hard to setup such basic features.

I don't mind sinking up to $350.

So, any ideas for devices, anyone? Pointers to information aggregators or additional search query recommendations are welcome as well.