Sounds like even someplace closer like Mars is going to take an impractically large receiver.

The Sun is roughly the same distance from Earth all the time, because we have a roughly circular orbit around it.

Mars is sometimes closer to us when our orbital position around the Sun is on the same side as Mars, however due to the different year lengths on Mars and Earth, sometimes it's much further away on the far side of the Sun to us.

I'm trying to think of any non-trackball / non-wheel / non-paddle stick-based arcade games that used analog controls from a retro time-period, and the only one I'm coming up with is Afterburner.

MAME can answer that question, more or less.

Under the MAWS deluxe search, change 'controls' to 'stick' which is MAME-ese for analogue joystick/yoke. You get this list including things like 720, Enduro Racer, Paperboy, SW/TESB/ROTJ, Space Harrier and Thunder Blade to pick a few classics.

To respond to the original question about joysticks, a lot of people build their own arcade sticks. The parts are readily available and the build doesn't need to be hard.arcadecontrols.com is a great resource and community for scratching that itch.

The truth is though that every type of home system is/was different, and the controls that suit a Commodore 64 and nothing like what suits a SNES, or an N64. If you're trying to recreate original-feel controllers for even a handful of emulated systems, it's going to be a lot of hassle obtaining them all, let alone getting them to work. A decently-made fighter stick plus an X360 controller should be enough to cover most bases most of the time.