'Enjoy your meal' is a bit of a flawed translation as this is more like the French 'bon appetit' - something you say to other people at your table when they are about to eat, not just something a waiter would say to you in a restaurant as they hand you your order. We don't have an equivalent phrase for this in English but Romanians and Moldovans say this all the time!
Honestly, if bon appetit isn't accepted, it probably should be. Maybe it's a regional thing, but no one I know says "dig in", though I'm aware it wouldn't be unusual. I probably hear "bon appetit" much more than "dig in", which I've definitely heard much, much more than "good eatin'".
Just "Enjoy" should also be accepted, however this is a complicated phrase with no direct translation to English. Like the Japanese say Itadakimasu to themselves to eating, the French say "Bon Appetit" to someone who'll eat, which is directly translatable to Romanian (Italian, Portuguese, German and other languages as well).
In Spanish, the most used expression would be "Buen provecho!" which has the same meaning, but with different wording as "provecho" means "advantage", "gain", "profit"...
In English, I believe that "Enjoy", "Enjoy your meal" or the widely spread loan "Bon Appetit" should all be accepted, despite the direct translation being "Good apetite".
The issue is that it is rare to hear a native English speaker say "Enjoy your meal". For decades, in the aftermath of the Second World War, food was rationed in the UK and British cuisine plumbed new depths of tastelessness. Food wasn't remotely enjoyable so no one ever suggested anyone should try! "Enjoy your meal" is used, but usually not a person who is eating with you. Normally, a waiter would say this having brought your meal to the table.
In modern Britain, we probably say "Bon appétit" (from the French) more than anything else. We even pronounce it exactly as the French do. However, despite British cuisine regaining much of its former glory, it is still not an ingrained tradition to wish someone an enjoyable meal, like it is in so many neighbouring countries. But then, it is also no longer so traditional to sit down and eat a meal together as a family - many people eat on the go.
Personally, I really wish that we could regain a more Mediterranean or Scandinavian style existence where sharing good food is the ultimate social interaction.
My experience of food in Romania was extremely good. The country is very agricultural and that means fantastic produce and people that haven't forgotten excellent, traditional cooking. Highlights for me were sarmale cu mămăligă şi smântână, ciorbă de burtă, mititei or mici and papanași.
Other expressions you might hear in the English speaking world are:
Bon appetit Enjoy your meal Enjoy Dig in Grub up Let's eat Eat up
It is a very sad indictment of the state of British cuisine, in the post war era, that the only true expression we have for poftă bună is bon appetit. Fortunately, things have greatly improved in recent years. Having travelled in Romania I found the food to be truly excellent!
"Enjoy your meal" should be the fraze taught, as you cannot translate this sentence literally. "Good apetite" sounds dodgy and non-english.... One could have an impression that "Poftă bună" means good apetite, while it's only a courtesy shout for anyone who is having a meal