You're either using the term incorrectly, or your overall claim is incorrect.

For example, minarchists are not in favor of universal healthcare, by definition - it doesn't fit the short list of the kinds of roles that minarchists believe government should play. There are plenty of people who are in favor of universal healthcare, who can't be called minarchists.

Well phrased.

This change neither increases nor decreases the size of the government, so it's unclear how you think "party of small government" is relevant here.

Colloquially, when people say "large government" they refer to the level and breadth of regulation, aka restrictions on private actors. This restricts private actors, so colloquially we say it made the government larger.

This reduces government regulations on contracts, not increases, a wider range of private contracts are allowed now hence this results in "smaller government".

If you mean this makes private corporations gain leverage over workers, sure, but that isn't what "large government" means.

There's two private actors here: private companies, and private workers. This explicitly restricts the mobility and freedom of private workers, and actively undermines the free labor market.

IMO this does fit the bill of "large government", as it's explicitly done to manipulate and pollute the free market.

"Size" can be power, not just headcount.