I've had to provide background references for a number of jobs in the past. This could well come back and bite you - what if the person hiring knows people from the company you supposedly worked for? It's a small world out there, in particular if you're looking for roles close to home.
Getting a job is an exercise in sales and marketing. Everything I've seen about OP's post and comments can be pitched in a manner that highlights learning and growth.
This isn't dodgy it's essential.
To be clear, I think you can do lots of dodgy things with a resume, but you can also craft a narrative without any of those things (e.g. claiming skills and experience you don't have).
The comment suggested:
> find some company that has closed shop in the past two months. Their HR staff etc. will be long gone, and who's to say if you worked there or not.