I also have the Kodi iOS app for controlling it with my iPhone. This is actually smooth and powerful, especially being able to use the keyboard on the iPhone for searching, but it suffers the same issue where I am not going to keep my phone turned on the entire time so there is a delay as the phone reconnects to Kodi so that it can then send controls.
This is where the HP MCE Transceiver comes in. For only $13 this device can receive and send IR signals from any remote that you have.
My HTPC is running Windows 7. So I installed WinLIRC and WinLIRC Helper. WinLIRC is a tool that allows you to interface with your IR transceiver in order to read in buttons that you press on your remote. WinLIRC Helper can then be used to map those keys into Keyboard keys or shortcuts.
When you are setting up WinLIRC, first right click on the exe and run it as administrator. Set the Input Plugin to be MCEVista64.dll. Then press the Create Config button and follow the directs the prompt window gives you. The directions will be to press random remote buttons until it is satisfied, then you will type in names for the specific remote keys you press. You cannot just use any name, you must choose one from this list of Name Space keys.
After that is complete, you will run the WinLirc Helper (while WinLIRC is still running as well) and map the controller keys to specific keyboard keys that you want. You must keep this running at all times.
You can have both WinLIRC and the WinLIRC Helper run automatically at startup by going to Start > All Programs > Startup > right click and select Open. Then create shortcuts for those programs and drop them in this folder.