As PackageID stated you really should get the sheets cut on a plotting table. The plotting table needs to have a reciprocating head to cut corrugate. Some places have plotting tables without the reciprocating head and that’s only for paperboard.
You should use cold glue to maximize the strength of the bond. The hot glue will not be suitable for large surfaces. When you use the cold glue, use a minimal amount to avoid the board from getting warpped. Do not use rubber cement because you will not get the appropriate bond. We use a formulated white glue like Elmer’s.
I notice you have the fluting in a different direction which doesn’t really do anything to enhance the strength. The fluting needs to be along the same axis in which the most force will be applied.
If you can specifiy the board grade, make sure to ask for mullen board and not ECT. The fibers in mullen board is multi-directional which makes it stronger along various axis. The ECT grade board has uni-directional fibers and it’s only strong in one axis.