A good question! Mr. Mojave. Now, your Korean has nearly reached advanced Korean level. Maybe you already know the meanings and usages of the connective ending '-(으)면서' and the noun '가운데'. So, I will skip detailed explanation about them. The connective ending '-(으)면서' can be replaced with the expression '-ㄴ/는 가운데(에)' only when it is used in supplementary background information, like a preposition 'amid' in English, meaning "While a certain event or situation is happening". You should consider the usages of the noun '가운데', since it can mean 'the middle, center, or among, amid' in English.

Wow. This is hard. So... we don't say '가운데' often, but I rarely saw this word in the books. So '가운데' is more like written language. Also, I would say '(으)면서', '가운데' has different perspective. When you use '(으)면서', it is focusing on the 'subject.' For example... 철수는 책을 읽으면서 우유를 마셨다. (Cheol-su drank milk, reading a book.) 나는 걸어가면서 생각했다. (I thought while I was walking.) 우리 가족은 저녁을 먹으면서 TV를 보았다.(My family watched TV, having dinner.) So.. these three sentences are focusing on what 'subject' does while 'the subject' is doing something else. Simply, there is only one subject for two acts. But '가운데' seems like it is focusing on 'atmosphere'. For example... 음악이 연주되는 가운데 연극이 시작되었다. (The play began, while the song was played.) 많은 사람들이 입회한 가운데 계약이 시작되었다. (The contract was signed, while many people were attending.) Like you see here, '가운데' is more like... explaining the situation, or surroundings. I hope my answer helped you.