I don’t have enough experience with CEC, but there are some CEC options in the settings to play with (in “Settings > System > Input devices > Peripherals > CEC adapter”).
Maybe you can optimize it a bit.
Did you try moving the timeshift path to another location (e.g. an nfs share or attached USB HDD)?
I assume the sd card is just too slow to handle timeshift and you need a pretty fast storage for writing and reading tv streams at the same time - especially HD streams.