Tous les exemples que vous citez dans votre 1er point signifient à peu près la même chose, et pourraient être utilisés comme titre de l’article.

Ici ils ont employé la phrase.

Les médecins veulent resserrer la loi

Principalement pour renforcer l’implication des médecins à vouloir que cette loi soit plus sévère. Je suppose pour susciter l’empathie du lecteur pour les médecins, dans cet article.

Using “vouloir + infinitive” when one lacks the power to personally take the desired action seems, to me, somewhat presumptuous, which is probably why I think I would have preferred either:

2.Les médecins veulent voir la loi resserrée or

5.Les médecins veulent que la loi soit [resserrée]/plus sévère

as the article’s title.

Although the addition of “faire” in “3. Les médecins veulent faire resserrer la loi” seems to render that option more doable/less presumptuous than the original title (Option 1) or even Option 4 (with its use of “rendre”), I still think either Options 2 or 5 capture best the doable/unpresumptuous goal/notion of “… réclamer un meilleur contrôle des armes à feu au Canada …” found in the article’s body.

Please note that, in my opinion, the presumptuousness that I detect in the original title would disappear (alas, along with its “idiomaticness”) if “vouloir + [a not doable/not permitted] infinitive” could be changed to “vouloir + the noun form of that same undoable infinitive,” i.e.,

1. Les médecins veulent le resserrage de la loi.

cf: This article’s title using “vouloir + resserrer” (similarly, along with “réclamait” in the article’s body) where President Obama had actually already announced his intention to, by Executive Order, accomplish the desired “resserrage.” (so the President, unlike the Doctors, had the power and was about to use it, making me tempted to wonder why the title used “vouloir” instead of “aller”: “Barack Obama va resserrer le contrôle des armes aux États-Unis.”