Logitech MX Keys sends incorrect modifier keys

I’m running CentOS 7 on a Dell laptop. The native keyboard works correctly, but my Logitech MX Keys keyboard is sending some incorrect modifiers:

• Pressing L WIN triggers L ALT
• Pressing L ALT triggers L WIN
• Pressing R ALT triggers R WIN (the keyboard lacks R WIN)
• Pressing R CTRL triggers R ALT
• Insert key is not detected at all

Default xbkmap settings:

$ setxkbmap -query
rules:      evdev
model:      pc105+inet
layout:     us,us
variant:    ,
options:    terminate:ctrl_alt_bksp

I tried using options to fix the problem:

$ setxkbmap -option altwin:swap_alt_win
$ setxkbmap -query
rules:      evdev
model:      pc105+inet
layout:     us,us
variant:    ,
options:    terminate:ctrl_alt_bksp,altwin:swap_alt_win

This fixes the left modifiers and R ALT, but now:

• Pressing R CTRL triggers R WIN

So I took a stab at combining another swap option:

$ setxkbmap -option ctrl:swap_rwin_rctl
$ setxkbmap -query
rules:      evdev
model:      pc105+inet
layout:     us,us
variant:    ,
options:    terminate:ctrl_alt_bksp,altwin:swap_alt_win,ctrl:swap_rwin_rctl

But that made it worse:

• R ALT triggers R CTRL
• R CTRL triggers R WIN

I looked through the options at /usr/share/X11/xkb/rules/evdev.lst, but can’t find any that address my particular situation.
I’d prefer a persistent solution, but I’m willing to add it to my startup scripts if need be.
I don’t use the native keyboard, so I’m ok with a solution that breaks it.