The dictionary will tell you that they are synonymous; I will tell you that "meanwhile" is more common than "meantime", unless you say "in the meantime". I would use "meanwhile", but "in the meantime" is a close second, with "meantime" dead last, in my opinion.
The mean in meantime and meanwhile does, as you suspect, come from the same root as the word meaning mathematical average. The original meaning of this mean is middle, and, with respect to meantime, it branches off to meaning intermediate and then further off to mean 1: Intermediate in time; coming or occurring between two points of time or two events; intervening The mathematical meaning also ...
in the meantime the period of time between two things; the period of time between now and when something is supposed to happen. -- Free Dictionary for the time being if you describe how a situation will be for the time being, you mean it will be like that for a period of time, but may change in the future -- Free Dictionary I believe that they are essentially interchangeable.
"Meantime" is a noun and an adverb, not an adjective. As I do not understand the true meaning you are attempting to convey, I cannot provide advice on how to correct your statement.
Using "meantime" as an adjective - English Language & Usage Stack Exchange
It is said to have a historical origin as preposition, but it is definitely not one today. Should the negative particle "not" be classified as an adverb? Should adverbial particles be classified as prepositions? Nobody knows. What do we call them in the meantime? Particles.