Carpet or not?

[wildebus]

The stud fittings are simply screwed through the fitted carpet into the wooden flooring beneath.

The stud top fittings for the mats are crimp fitted through them.

The tricky bit is getting them correctly aligned. I used a large sheet of paper laid on the floor and cut to shape, then placed the mat on top, punctured the mat in the required positions for the stud tops, then marked the paper through the holes. Then I used an awl to make pilot holes through the carpet and fitted the screws.

Then I removed the paper, fitted the floor stud fittings one at at time. Finally I crimped the stud tops to the mats through the holes made earlier.

It sounds more complicated than it is, but the end result is mats that are held in position permanently.

Your solution sounds like the most initial work BUT overall the best and safest way.
Are these studs similar to the type of studs used to secure drivers floor mats?

 

[Canalsman]

They are press studs which are used for all manner of things.

This sort of thing:

25sets Stainless Steel Canvas Snap Fastener to Screw Press Stud Marine Canopies | eBay

You need to ensure that the dome section has a central pillar long enough to go through the mat and then be crimped over using a hammer and crimping tool.