Flatness Measuring Device for Press Platen With Limited Headroom

Something in a laser scanning flatness tester, perhaps?

Canon LSF 500 Laser Scanning Flatness Tester | LV19860542

May I suggest in the interest of clarity that in future posts you stick to one system of units. Your post uses inches, feet, metres, millimetres and thousandths of an inch.

Very confusing.

The only two countries in the world that still officially use imperial measurements are the USA and Myanmar so if you aren't in either of those countries then I'd suggest sticking to metric units.

The best option is to do what I do and use metric units as the primary and then include imperil units in brackets after the metric. For example:

The steel rod had a diameter of 10 mm (0.394 in) and a length of 350 mm (13.780 in).

That way everybody knows what you are talking about.

I would build a dolly longer than the variation distance using steel wheels and carrying 3 dial indicators. Place one at one end of the dolly, one at the other end of the dolly and one in the center. Roll it along the length of the platten and note the variations between the dials.

.001" is very little tolerance. What are you making that needs to be that flat over that length? What material could maintain that flatness once removed from the press?

Carbon fibre perhaps?