TWRP after 2.4 supports exfat. What version are you using? Many people have posted that TWRP 18.104.22.168 has hosed sd support and people have posted earlier versions like 2.6.*.* and now 22.214.171.124 work fine. I'm guessing you've were trying a broken version.
Your phone is a computer running the linux operating system. Hardware works by way of software called drivers that allow the system to communicate with various devices like drives and radios. The drivers in linux are built into the kernel which is the heart of the system or they are loaded as modules. When building a kernel you can add or subtract any number of various drivers you may or may not need into the system. The stock Samsung kernel has the various file system (fat32, exfat, ext3, etc) drivers built into it and that's why your sd card is recognized and works fine within the Samsung custom Android operating system you're running. TWRP and other recovery systems are bare bones operating systems that you load in order to perform maintenance functions like loading firmware or running backups. When the devs for TWRP compiled their kernel (processed all the changes to their new kernel and made it ready to operate) for version 126.96.36.199 they screwed up by either leaving out support for cards of a certain size, file systems of a certain size, support for certain filesystems or used experimental buggy drivers. This is why your card doesnt work in recovery.
You should try a different version of the recovery you desire. You might also want to try formatting the sdcard as another filesystem like ext4. The CWM thread for your tablet forum.xda-developers.com/showthread.php?t=2432467 says that 64gb support is very buggy and that CWM is not being worked on anymore for your device. Some people say it works for them though. Page 1 of the TWRP thread for your device (which is final on version 2.7 which may mean his last build killed 64gb support) mentions earlier versions working with 64gb cards. You may want to ask people posting early in the thread if they have an early version they could upload for you.
If you own a mac or linux system or burn a linux cd( ubuntu live cd) you could format your 64gb microsd as ext3 or ext4 and it should have no issue unless it's a problem with the capacity of the microsd in which case you could try to create one partition on the microsd card of say 25gb. That could work if partition size and not disk capacity is the problem.
Those seem to be your options along with just buying a 32gb, 16gb, 8gb, 4gb, 2gb card to root with. Memory is getting cheaper and images to flash ROMs and recoveries are generally small. You could probably buy one in your local drug store for $5. If money isn't tight, there's your easiest solution. You could borrow a smaller card from someone too if money is tight. They are pretty common in phones going back 6 years now. If you want to learn more about your phone and get hands on experience try another method above.
Good luck. Hope you get it going.
LG G3, GS5,
GS2, G Tab 3, G Tab 10.1, iPhone 5S, iPad Air, Kindle FireHD, Nexus One, Nexus 4, Nook, Palm Pre, Sensation