Good news for everyone having difficulties sourcing the Si4362 radio IC.
I verified that the transceiver Si4463 works with dAISy. This probably also applies to Si4460 and Si4461. Besides being more widely available through distributors, more adventurous souls can even find these ICs on Aliexpress.
Even better news for those that want to recreate my project with minimal effort: Si446x based radio modules are sold on eBay and elsewhere.
I bought the E10-M4463D from eBay for $7.99:
I chose this module over others because all pins of the radio are broken out to headers.
Unfortunately two pins (GPIO2 and GPIO3) are reserved to control the RF switch that connects the antenna with RX or TX channels. But after a few minor changes to my code I had dAISy working.
Here's the branch on Github: https://github.com/astuder/dAISy/tree/E10-M4463D
The wiring changed:
GPIO0 -> P2.0
NIRQ -> P2.5
GPIO2, GPIO3 -> no longer connected to the LaunchPad
As the modules are built for 433 MHz and AIS is using 162 MHz, I had to replace antenna and passives on the RX side.
The new passives from left to right are (ignoring the obvious 0-ohm resistors) 11pF, 150nH, 13pF. As you can see the 0603 components are a very tight fit. I reflowed them with a hot air station instead of using a soldering iron. The clunky thing on the right is a BNC connector, SMA probably would have been a more elegant fit
Technically, it's still not ideal. The traces might be impedance matched to the original frequency. However a quick real-world test demonstrated similar sensitivity as my original breakout boards.
EDIT: added wiring information
EDIT: added link to Github