I'll just nip of to the market, then. brb.
Lovage: Easy to get hold of if you're in Europe according to Wikipedia "its flavor and smell can be described as a mix of Celery and Parsley, but with a higher intensity of both of those flavors". So, literally just add in a large amount of those to compensate for the strength.
Caroneum: According to this website[0] "as long as you can find a carton of white grape juice, you're set" to make it, so that's readily available.
Rue - According to Wikipedia "Rue extracts are mutagenic and hepatotoxic". It's bitter, so you could very likely substitute a fair amount of Fenugreek for it, which is bitter but fragrant.
Laser Root - Also known as Ailphium, this no longer exists. However, Asafeotida "had similar enough qualities that Romans, including the geographer Strabo, used the same word to describe both". So literally just use that.
So in other words you use Pepper, Cumin, Coriander, Celery, Parsley, Homemade Caroneum, Fenugreek, Asafeotida, and Honey.
Which really doesn't sound that difficult to get hold of, does it?
[0]: https://pass-the-garum.blogspot.com/2013/03/caroenum.html
Please don't use pure asafoetida, I don't know of anyone else that does that and it will just smell horrible, along with giving you stomach problems. Even forms of asafoetida you can find in non-western countries are typically mixed with rice flour.
https://www.pureindianfoods.com/hing-asafoetida-powder-p/hin...
Interesting, because every single report I've heard on it has said the opposite! I don't distrust you, I'm now just wondering what causes the variation!
The author substituted diced dandelion greens for the rue.
I find it pretty amazing that other than the toxic ingredients most of the foods and spices from 2000 years ago are the same I have in my cabinet. Probably taste similiar enough. I bet freshness matters more than whatever changes occurred. It was striking how different fresh coriander seeds from cilantro plants in my backyard tasted compared to the dry stuff at the store.