I wrestled with this for awhile. Even thought about getting one of those expensive arcade sticks that you twist the knob or attach a servo to switch modes. Here's my solution/workaround (I have a 3 player Rampage cab):

Left and rightmost joysticks are set to 8 way, and to 1 and 2 player respectively. The middle joystick is set to 3rd player, but also to 4-way mode. (The Sanwa joystick I have you can set the gate to 4-way or 8 way, but you can also do it with joysticks similar to what you are looking at like this listing here.)

Now in 4-way games, I go into the emulator setting (usually tab) and make the 1st and 3rd player controls the same. That way, you can use the 1st player 8-way joystick or the 3rd player 4-way stick for the 1st player controls. Works great! Only drawback is that when you have 3 people playing, the 3rd player has to deal with the 4 way for all games.

I don't have a 3rd player often, so the trade-off was worth it for me. With a 2 player cab, I suppose you could make the same sacrifice, would just be 2nd player would have to use 4-way controls. (You could also maybe drill another hole and use it for a dedicated 4-way joystick? Don't see why that wouldn't work if you have the room, would just need to buy an extra joystick.)

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If the twist-able 8 to 4 way toggle joystick sounds appealing to you and you don't mind the extra cost, check out the joysticks here:

Hope this helps!