Why did Moses take possession of so much land east of the Jordan before the 2 1/2 tribes asked for it? Maybe so there'd be no enemies at their back while they invaded Canaan and to allow some time to settle before having to worry about a counter invasion.

Moses led the army east of the Jordan because that campaign was still considered to be part of the wilderness journey and preparation phase. Joshua took over after they crossed the Jordan because he was the chosen leader for the conquest.

Joshua 12:1-6