Or, if your original neg is 35mm and your enlarger goes to 6x6 or more, you can enlarge your 35mm frame to a piece of 120 film, taped flat on the easel. With f/22, start experimenting with the exposure at something like 1 second. Then, you can enlarge from that neg. It is not that tedious!
Or, just tape down a piece of unexposed film in the same format (or larger!) to the easel in dark, then put your neg on the top of it, and add a sheet of glass. Expose with the enlarger to make a contact copy. This is not that tedious, either!
If you happen to have orthochromatic film, this is even easier as you can do it red light on.
This way, you won't have any problems with paper texture and you can vary the size or make further copies more quickly. But well, there's nothing wrong with the way you describe, but I think it's not much easier, and the contrast may be too high.