For plugs -- the generic "2500 Series" connectors (2.54mm / 0.1") only goes up to 25 pins. Most sources have the tooling but don't stock 21 through 25-pin versions, these are usually special ordered.
For 28-pin connectors - myself and another seller paid to have custom tooling created to make the 28-pin plugs. The fee for custom tooling is why the 28-pin plugs cost considerably more than the smaller sizes. PBR has a huge quantity of 28-pin plugs so he's a good source for them. I still have about 9000 of them left but these are destined to be sold with the rest of the business.
For these plugs as genuine Molex parts - the part number is 22-01-2xxy
"xx" = number of pins. 02 = 2-pin, 03 = 3-pin.... 28 = 28-pin.
But Molex now only makes 2 thru 16-pin plugs.
"y" = lock/polarization style
1 = No locking Ramp, No polarizing ribs
5 = Has both locking ramp and polarizing ribs
7 = Has locking ramp, no polarizing ribs
For pinball - the optimum style is "7". Can be used with or without a locking type header.
So a 16-pin Molex = 22-01-2167 but a 22-01-2165 or 22-01-2161 would also work.
There is a similar part series from Molex -- 22-01-3xxy. Essentially the same connector but the last digit for lock/polarization style is different.
The LCSC connector link posted above does not go to a 28-pin plug but goes to an 18-pin plug instead.
Swinks mentioned the way to go for many of the obsolete connectors -- 3D printed. There was somebody (maybe Swinks?) that recreated the nearly impossible to find edge connectors for Gottliebs.
Header lengths -- Molex plugs were intended to work with 0.320" (8.13mm) mating post length IF you are not using a locking header. An example of this would be Molex 22-28-4361. There are many pin lengths out there (e.g. Molex 22-28-4360 with pin length of 0.24") they will work but are a bit too short and the connector doesn't fit real solid. If you are using a locking type header with friction lock plugs then you can go down to the 0.240" mating post length.
i used to sell custom made 0.320"/8.13mm headers but the 9.5mm headers mentioned above would work just fine. If possible, should order them with tin plating and not gold flashed.