2 UART connected on the same port
Since you need to be connected to only one device at a time, you could use a multiplexer to switch between the two chips, like the NX3L2467:



You only need a DPDT switch; this is a 4PDT one so you're only using half of the circuit.  But all of the DPDT switches I found had very unfriendly packages to work with such as VQFN, BGA etc.  This part comes in a 16-pin TSSOP package; not as nice as a DIP to work with but doable.  You can get TSSOP16 to DIP adapters. It also has a very low on-resistance (0.5Ω).  It will work off of 3.3V which I assume is your supply voltage.