Cartridge dumpers generally don't work with carts that have circuitry beyond the main rom chip. At least that's the situation (now) with the Retron77. It seems to be somewhere around 70-75% compatible. Cartridge dumpers feel cheap to me. All the hard work is done by the emulator developers. All the manufacturer does is build the shell and interfaces. But to be fair, the compatibility level of the Retron77 goes up if you use the microSD card and roms.
One core that seems popular is the A2601, it works on the MiST or other similar hardware if recompiled.
And you should simply do a search on "atari 2600 fpga cores" to get many more links. Some will even link back here to AA.
By weird cases I mean mounting the board and its associated in something that precludes having the proper 6-switch available. Some projects rely on on-screen controls or even require you use a controller different than the standard 2-axis 1-button Atari Joystick. Some projects put the cartridge in in non-ergonomic manner or prevent some oddly shaped carts from fitting at all. Some projects may simply not bother with external connectors for controllers and rely on built-in controls - so you don't have the ability to use the keyboard or driving controllers or trak-ball/mouse, or any hacks.
There aren't any secrets about the VCS being kept hidden or anything. All the information is there, on the internet. Much of it here on AtariAge. The source code for the FPGA cores is on github. The PCB schematics and TIA internal schematics are available. The sources for Stella emulator are on github. The 6502/6507 is a well-researched and documented chip. The RIOT is pretty straigtforward and still made today IIRC.
So making a clone of the VCS is just matter of bringing all the details together, and doing it in an economical fashion.