A few remarks:
Rome-trieste is 700 km. No way the assasin would be able to reach the border at 4:45 pm. Especially not with an Eastern bloc car and with frequent toll booths which were inefficiently operated with delays at the time.
Further the border crossing at Trieste was always very busy with huge queues and a lot of police. The border was open with a lot of traffic with tourists to Yugoslavia and Yugoslav people shopping in Trieste. There was only a two-lane road jamned with a queue of often a kilometre.
The KGB or Stasi would never organise a high-profile assasination with the assassin racing hunderds of kilometers in a suspicious car with Eastern Bloc numberplates.
Yugoslavia was independent from the Eastern Bloc and has many catholics. They would never cooperate with such a plan, especially if the non-interference at the border would make their complicity ovvious.
Yeah, the Jugoslavian authority not even trying to stop him it's the basic equivalent of going in television and admit that they are involved in the assassination...and frankly the east intelligence services will be already considered the guilty party by everyone even without strong proof.
The use of a never before heard catholic terrorist group will be usefull only in convince the usual faithfull but for that just the soviet secretary saying that they are not involved it's enough and i doubt that the general population will go for it.
Frankly for the killer the better way is to eliminate him just after the attack and bury the corpse, even trying to stay quiet in Rome for some days will be extremely difficult, with the Pope dead the entire police force of Italy will be used to search home by home the capital...and an east european car is a big red flag, unless is a Yugo in that case can pass for an italian car at first glance as they were basically Fiat Knock off