I wouldn't do it if it were my system. I like to keep my hardware period correct. Everything down to the mousepad (if it needs one) is usually period correct to my machines. But, if you want you could do it. I like tandy computers. I have 2 of them and they are both pretty damn cool 😀

I thought the Tandy's CPU was already starving for memory bandwidth with the video hardware also taking it's fair share of that.

Here's the deal.

Simply replacing the CPU and the crystal will not be enough. You will need to replace many things on the motherboard to ensure everything is rated for 20MHz operation, including the DMA controllers, memory, bus controller, ready interface etc. If these things are part of an integrated chipset, then this is not possible. In the early days of integrated chipsets, they were very sensitive and less reliable. Often times the maximum operating speed is stamped into the top. If you were to run a chipset designed for 8MHz at 20MHz, you would risk frying it. If your system does not have a chipset and uses discrete logic, most of the chips on your board will be able to handle 20MHz, with the exception of the few I mentioned. However, even if you replace all of these components some timings will still be off. The ISA bus for example will run at 20MHz rather than 8MHz. most ISA cards can't handle that speed. Unless you know how to design a bus divider circuit, I wouldn't bother. Also, if your system uses 0 wait state memory, it will be quite difficult to find replacement DIP RAMs that can function at 20MHz with 0ws. The best solution for running at 20MHz would be a clock doubler circuit that sits between the CPU and motherboard. I have seen this product for 8088s and 386s, but not 286s. It might be possible to build one though.

That's what I was thinking, run only the CPU at 20mhz and everything else at 8.
I'm not quite sure how to do that, though. I've got full schematics so I might
be able to come up with something.

There is a public domain clock doubler circuit for 8088. I think it's called "PC Sprint". Here is a link to it:

http://www.brutman.com/pcsprint_annotated.zip

You may be able to get some ideas by studying it. I'm not sure how adaptable it would be to the 286 platform.
User "Feipoa" attempted to develop an external clock doubling circuit for 486 chips using a PLL, but it was not successful. Might be worth asking about though. It might be easier to develop a doubler using a PLL for a 286 since it isn't as complex and runs at a much lower frequency.