We've seen the different methods of replacing a timekeeper chip... What do we recommend?

That depends on the player and if you want to re-use (i.e. hack) the old chip. As a rule of thumb: Always fit a socket, that makes future replacements easier.

Basically there are two options: Replacing the chip with a new one, a 1-on-1 replacement, either directly on the pcb or in a socket. And the second option: Drilling a hole to show the connectios, and installing a parallel battery, a CR2032 (also in a battery holder). In my opinion, desoldering the chip and installing a socket with the exact same pins is the easiest method. There are good desoldering tools to make this easier to do. Downside is that you have to install a new chip every X years. These chips will costs around 25 dollar, will last around 10 years. (if you're lucky) - Some sources of these chips have bad storage places which shortens the lifetime. You can't always trust the source of these chips. So pro: it's easier. Con: costs more money and returns every X years. 

Now on to the second option, the parallel battery. You have to use a dremel to reach the battery contacts inside the chip, that's a tricky part. Once you have succeeded in this and you have soldered two wires from the plus and the minus: The battery holder you glue somewhere on the board, and all you have to do is sliding in a new CR2032 battery. These batteries are cheap and can be bought anywhere. So Pro: It's cheap, it's easier to maintain. Con: It's more difficult to get this done, you have to carefully dremel inside the chip. In principle all timekeeper chips are the same with the same number of connector pins. Be careful that you take either a 8kb version or a 32kb version.