Just my 2 cents

The officer is claiming he could not keep up with you. ask how fast he had to go to catch you.

This is simple math imo.

someone doing 43-44, the cop would not be able to catch you if he was doing the same speed, thus he would have had to go faster to catch you. the quicker he wanted to catch you the faster he would need to go.

How far behind you (when he "caught up") til when he hit his lights? ie. how long was he "pacing" you?

Also was this a marked construction area? were there signs stating construction zone ended?

Just some things to help your case poss.

good luck.