There are two routes for outboundary Travelcards issued from Cambridge.
ANY PERMITTED - valid on any train for a return journey between Cambridge and the boundary of Zone 6, and then unlimited travel on any operator within the zones. The main reason to buy this more expensive ticket is if you want to travel on Great Northerm
AGA TRAINS ONLY - This ticket is cheaper and I suspect this is what you are thinking as the 'Liverpool St' ticket. Between Cambridge and the boundary of Zone 6, this is only valid for a return journey on trains operated by Abellio Greater Anglia.It is not valid between Cheshunt and Turkey Street on London Overground-branded trains as they are both outside Zones 1-6 and not run by Greater Anglia. If you happen to find a Greater Anglia service going via Turkey Street, then the ticket would be valid on that service, but my understanding is that they are quite rare nowadays.
Changing onto the Greater Anglia slow service via Tottenham Hale is of course perfectly allowed