The PVR-350 card came with a remote control (as seen in an image in this post), model number A415-HPG (found under its batteries). I selected "Hauppauge Remote" (16) and then "Grey Remote" (b) when setting up MythTV.

After that lirc will see the remote through the IR sensor but the buttons are not mapped correctly. Using the lirc config files in the post by Russ in this thread will fix most of the mappings – though there is still some tweaking to be done.