I do not know were you are moving your layout sections around but I thought I would share how I solved the problem of moving heavy train board sections.
I build my layout out from 1 x 6 inch for frame and the top was 3/4 inch particle board, very heavy. I knew my layout would be set up on the floor for 1 month a year and then stored, against the wall in a garage. It also was moved from Jamaica to the states and then move 4 more times to different houses. I would be the only one moving it around the house but not up steps. I built-in wooden wheels on an edge to allow rolling around with help of handles under the board. The only heavy lift is when the train board is on the floor and must be stood up. This is done with care to keep a straight back and lift with legs. The train board sections were stored against the car port wall and then laid on the floor as necessary. Much work, like wiring, was done with sections standing against the wall.
6 inch diameter wooden wheels were made from 3/4 inch plywood sealed with Elmer's glue to allow moving of the board sections by one person. The wheels were installed, with 1 inch diameter wooden dowels for axles (paraffin wax for lubrication). One wheel is on a corner and another is down the side about 2/3 to the end. This allows the board to be turned and pivoted around this wheel. Handles from 1 inch diameter dowels were installed under the board along the edge to allow steering and lifting when moving.
The layout sections were small enough to store and ship in mattress boxes when we relocate due to work transfers. They are small enough to go through standard size doors and up steps.
The main board length is 11 ft, 1.5 inches in length and width is 5 ft, 9 inches The section with the control panel is 6 ft, 3/4 inches long. The other section is 5 ft , 3/4 inches wide.
Corner wheel
Side wheel - This wheel is doubled up as this section has the control panel and all the transformers, so it is very heavy.
I might say the particle board is fairly quiet. The train board expansion, to an L shape, was covered with 1/2 inch plywood and very noisy. I wound up installing slightly over sized tie, pieces of truck inner tube under each tie and switches that quieted it down to about the same as the particle board. I doubt it as quiet as Homasote.
Charlie