@Bastien_Siebman, I have two suggestions:
Recently I started doing this (in the past I used the method you outlined of Later/Due Date/Assign to me): Multi-home the task into a Pending project and also a specific section in there. Use sections for Weekly, Monthly, Yearly, and whatever other special ones you want. In your case, you could also have 1st week of month (maybe eliminate this and just use Monthly for these?), 2nd week, 3rd week, 4th week sections. For each section you need a single recurring task to remind you to look at that set of tasks, in case any are there, and triage/complete them. The simpler version I started using has been working well for me. This share some similarity with your add project idea but I prefer the single project.
The other approach is to assign a tag like Snoozed-Tomorrow, Snoozed-2Weeks, etc. and set up Zapier rules. I know that they have a rule when a tag is assigned; not sure offhand what date calculations are supported/needed, but worth a shot.
Hope that helps,