Only the first four controller devices are available to be selected

Product: Star Wars: Squadrons
Platform:PC
Please specify your platform model. PC
What is your gamertag/PSN ID/EA Account name? J_Lunchbox
Are you playing in VR? Yes
Which VR Platform are you using? Steam VR
Which part of the game is the issue happening in? Game Menu
What were you doing when the bug occurred? Step by Step detail is helpful. Trying to map game controls to my flight controllers
Where did this issue occur? Please include menu name or in game location. control mapping meny
When did this happen? (dd.mm.yy hh:mm) 2020-10-02:20:00:00 NZDT
How often does the bug occur? Every time (100%)
How severe is your issue? Can't play
What happens when the bug occurs? Game controller unavailable for mapping
What do you expect to see? My game controller amongst the list of mappable controllers.
Which ship were you playing? If not applicable, just answer "no" or "none." none
What components were you using? Was trying to use Warthog Joystick and Throttle and VKB Rudder pedals (without success) :-(
Which customizations (if any) were you using? None

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I have 7 game controllers attached, but the game only allows me to choose from (presumably) the first four it encounters when it enumerates the list of available controllers.
My flight stick, rudder pedals and throttle are apparently at the wrong end of that list and as a result are not made available for mapping in-game.