Sounds like the problem is you are trying to port from 3e where multiclassing was almost always more powerful than single classing to 5e where the two are more balanced without being willing to change your level progression. Instead of looking at doing the exact same thing and trying to get exactly the same output from a new system look at the whys of what you did and look at the tools you now have available to achieve those goals..
I agree with this. Converting characters from one edition to another has always been a mix of art and science. While some characters translate directly very easily (particularly single-classed martial types) others take some finagling.
I've been playing around with converting different characters from different editions (2nd, 3rd and 4th) into 5E and some move over very easily (particularly single-classed 2nd Ed characters. Select an appropriate background, eyeball their Non-Weapon Proficiencies into Skills, note their new class/race abilities and you're good to go.) and others take more work.
I had a dual-classed (Fighter 2) Thief 11 from 2nd Ed Skills and Powers focused on throwing daggers that I eventually converted over to 3rd Ed. Since there was no real "minor magical ability" option in 3rd Ed, I swapped one of his Thief, I mean Rogue, levels for a level in Sorcerer. I also gave him Quick Draw, PBS and Rapid Shot for the dagger-throwing. It wasn't perfect, but it kept the feel of the character. At the end of the campaign he was a Fighter 2/Rogue 11/Sorcerer 1/Homebrew PrC 1 with the Spring Attack chain as well. My dice playing the character, particularly in situations where he was gambling or the situation was a long shot, where almost consistently hot, to the point the character was referred to in game as being really lucky.
Converting him to 5E, I went over his sheets from both editions, and ended up with a Fighter (Eldritch Knight) 4/Rogue (Thief) 11 with the Mobile, Lucky and Skilled feats. EK was a bit of a stretch, since his 3E sorcerer spells were non-blasty and his 2E abilities were pretty much Detect Magic and heightened scroll use. But I stuck with Abjuration spells and took Detect Magic as his freebie, so it worked out.
Again, the character isn't a direct map from edition to edition, but the overall feel is there.
For the monk who used to be a rogue, unless those rogue abilities were a core aspect of the character (and with the only 1-for-1 ability really being Sneak Attack, I don't see how it is essential) I agree with the others that the Criminal background makes a lot more sense than a rogue dip.