It was certainly called HardHat
 

My brother and I are going crazy. Did we both totally fabricate these memories of this game?

I'm very, very certain it was just called Hard Hat. One word or two words I do not know.

The goal, as I recall, was to build architecture. There were steel beams and brick walls, windows and doors. The building was only made from one side, like it was a blueprint or a slice of the layers of flooring and what have you.

One key aspect was, you'd have to slide the field of vision up and down to see the different floors, and this silly construction worker mascot-type guy would say, "Goin' up a level!" and "Goin' down a level!" each time you did this action. It was immensely amusing to me as a small child.

Aside from that, I can't possibly remember any other details. Perhaps it was like The Incredible Machine, where you had only a few parts to finish a project? Maybe there was no goal, and you just build whatever crazy building you wanted. Either way, diving through Google was no help, as other games with "Hard Hat" in the name are apparently abundant and more contemporary.

Some day, I hope to reunite with this odd software. If only to hear that obnoxious man say "GOIN UP A LEVEL" once more

Hmm, I used to play some similar game on my ZX spectrum in the early 90s. It was beams and supports falling from the top, and you had to lift them and put, making floors... Main hero was construction worker indeed, and he taken about 1/3 of screen... Unfortunately, I totally forgot the name of the game, and World of Spectrum gave me nothing with obvious keywords (as hard hat, construction or building). *shrug* Maybe it will resurface later.