The chassis to engine earth strap is at the tail end of the gearbox and is made of something slightly less robust than wet spaghetti. An additional strap in the engine bay where you can see it is well worthwhile and not expensive.
Agreed, and better to have an earth strap from chassis to engine block as its to that the starter motor is bolted, so forming the earth return. Make sure you use the correct very flexible flat braided earth strap material for this purpose.
Using an ohm meter to check for earth strap integrity is not the best test in this case. The meter may show good continuity for the tiny test current but not necessarily when 300 amps for starter is flowing. A good visual and mechanical check for clean corrosion free bare chassis connection points is more valid.
Having said all this I still suspect the new battery. If possible a set of jump ieads from another vehicles battery, connected correctly and directly to the terminals of yours would prove the point, if there was a substantial improvement.
