L'entrée express est une bonne option. Vous pourriez être admissible aux tirages au sort des catégories française et éducative.
https://www.canada.ca/fr/immigration-refugies-citoyennete/services/immigrer-canada/entree-express.html
You and your spouse need to do your medicals and it will be submitted by a panel physician directly to IRCC, you can submit just E-Medical which will be provided by a panel physician.
Children don't need to undergo a medical in this case.
As for CUAET, be careful if you are still eligible for a work permit:
You can still travel to Canada using your approved temporary resident visa until it expires.
If you were also approved for an open work permit, you’ll get it when you arrive in Canada, as long as your letter of introduction...
For construction is more realistic but you will be eligible when you have accumulated, within the past 3 years, at least 6 months of full-time, continuous work experience (or an equal amount of part-time experience)
in a single occupation listed in the table below
in Canada or abroad
Check...
You can check if these if they are aligned with your duties. They are within stem category. But the score is rather high for STEM as well.
Occupation
2021 NOC code
2021 TEER category
Mechanical Engineering Technologists and Technicians
22301
2
Mechanical Engineers
21301
1