"Basically, is it permissible to insert any other modifiers between the relative clause and the noun it is modifying?"
Yes, it is. In fact, it is commonly practiced as long as the modifiers are not excessively long and/or elaborate. If they were, it would often look/sound more reader- or listener-friendly to split the information into two separate sentences.
I will take the liberty to alter your base sentence a little to make it more natural.
「もうすぐ[日本]{にほん}に[行]{い}く[友達]{ともだち}がいます。」 (No modifiers in between.)
"I have a friend who is going to Japan soon."
↓
「もうすぐ日本に行く、ジョンという友達がいます。」 (The comma is optional.)
"I have a friend, named John, who is going to Japan."
↓
「もうすぐ日本に行く、ジョンという(、)[身長]{しんちょう}2メートルの友達がいます。」 (Use of commas recommended.)
"I have a friend, named John and 2-meters tall, who is going to Japan soon."
One could add another short modifier or so within the same sentence between 「行く」 and 「友達」, but to add more would make the sentence look long-winded and difficult to follow.