A very cheap approach is to use the Xfinity 1067BC4 remote, using setup code 31306.  It is important to not buy the cosmetically similar 1067BX3.  Here's an example of the correct remote from eBay.  $5.50
You may need to contact a seller to verify that you're buying the correct remote.   The label inside the battery compartment should read 1167ABC1-0001-R or 1067CBC4-0004-R or RC1475511/01B.

31306 will control most of the functions of your HK, and it can be manually programmed to send any of the functions.  We know most of the codes.