I figured it out. There were two machine keys that were different between the machines that were able to connect and those that were not. I'm not too familiar with these, but I came across them in another post. I'm not sure if both are needed or just MachineAccessRestriction, but I was able to export the keys from the working machines and import them into the ones that were showing "Access Denied". After this, I was able to connect using Hyper-V Manager as normal.
I'm assuming my other machines that were able to connect did not have these keys modified when upgrading, but a fresh install of 1709 wrote different values.
The keys in question:
Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Ole\MachineAccessRestriction
Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Ole\MachineLaunchRestriction
Here are the working values that I imported into my laptop (these came from a working Windows 10 Pro laptop). Save the key below to a .reg file and open the file to import and overwrite these keys.
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Ole]
"MachineAccessRestriction"=hex:01,00,04,80,cc,00,00,00,dc,00,00,00,00,00,00,00,\
14,00,00,00,02,00,b8,00,06,00,00,00,00,00,14,00,07,00,00,00,01,01,00,00,00,\
00,00,01,00,00,00,00,00,00,14,00,07,00,00,00,01,01,00,00,00,00,00,05,07,00,\
00,00,00,00,18,00,07,00,00,00,01,02,00,00,00,00,00,05,20,00,00,00,32,02,00,\
00,00,00,18,00,07,00,00,00,01,02,00,00,00,00,00,05,20,00,00,00,2f,02,00,00,\
00,00,18,00,03,00,00,00,01,02,00,00,00,00,00,0f,02,00,00,00,01,00,00,00,00,\
00,38,00,03,00,00,00,01,0a,00,00,00,00,00,0f,03,00,00,00,00,04,00,00,a1,27,\
60,8f,9a,bb,18,34,63,b6,77,ff,9d,d5,b6,6c,e7,32,1a,68,08,52,43,92,86,a6,1f,\
d8,98,17,1b,3b,00,00,00,00,00,00,00,00,01,02,00,00,00,00,00,05,20,00,00,00,\
20,02,00,00,01,02,00,00,00,00,00,05,20,00,00,00,20,02,00,00
"MachineLaunchRestriction"=hex:01,00,04,80,d0,00,00,00,e0,00,00,00,00,00,00,00,\
14,00,00,00,02,00,bc,00,06,00,00,00,00,00,14,00,1b,00,00,00,01,01,00,00,00,\
00,00,01,00,00,00,00,00,00,18,00,1f,00,00,00,01,02,00,00,00,00,00,05,20,00,\
00,00,20,02,00,00,00,00,18,00,1f,00,00,00,01,02,00,00,00,00,00,05,20,00,00,\
00,32,02,00,00,00,00,18,00,1f,00,00,00,01,02,00,00,00,00,00,05,20,00,00,00,\
2f,02,00,00,00,00,18,00,0b,00,00,00,01,02,00,00,00,00,00,0f,02,00,00,00,01,\
00,00,00,00,00,38,00,0b,00,00,00,01,0a,00,00,00,00,00,0f,03,00,00,00,00,04,\
00,00,a1,27,60,8f,9a,bb,18,34,63,b6,77,ff,9d,d5,b6,6c,e7,32,1a,68,08,52,43,\
92,86,a6,1f,d8,98,17,1b,3b,00,00,00,00,00,00,00,00,01,02,00,00,00,00,00,05,\
20,00,00,00,20,02,00,00,01,02,00,00,00,00,00,05,20,00,00,00,20,02,00,00