Where is your FPM in the staple during approach and during flare? Are you aligning the 2.5 deg line with the end of runway and aiming FPM at the threshold - so not extending flare/touchdown to far? Are you touching down at and holding 13 deg the whole way? Are you aware you can extend the SB to the standard 60 deg by holding the switch in the open position while gear down (so further than the 'allowed' 43 degrees to prevent hitting ground during touchdown/aerobrake). The SB opens fully again by itself once the nosewheel is on the ground.
Batumi is an 8,200ft runway, and the reqd landing distance of an empty F-16 is approx 3-4,000' (depending on alt/temp/wind) with max braking - so you should have ample space to land and stop if you are performing the approach/landing correctly.
I wouldn't count on DCS to have accurate drag simulation to effectively use aerobraking, but I have never had a problem stopping the Viper. The max nosewheel speed is around 217 knots so if you wanna gently drop it earlier and THEN get on the brakes feel free - aerobraking is just free decceleration and you SHOULD have plenty of room for it.
VampireNZ's post in F16 Landing Question at Batumi air base on Caucasus MP was marked as the answer