Where do you draw the line between straight and variety cryptics? I’d put it at making alterations to the clues before you solve them, or making alterations to the answers before you enter them. Another definition might be that if you have to give special instructions to the solver, that apply to that specific puzzle, it's a variety cryptic.
That still leaves plenty of opportunity for constructors to be inventive within the straight cryptic format. Cross-references are probably the most common such element. They’re quite common at the Financial Times and other British puzzles (including LizR’s). Sometimes they provide an opportunity to group answers together around a theme (which is usually made apparent in one of the clues–to by custom one of the last acrosses); other times they’re just a chance for some different wordplay.
3,337 was one of those, and I don’t think I’m giving anything away by noting there happen to be a lot of arabic numbers showing up in the clues this week. It’s up to you to figure out what the connection is, but if you’ve done cryptics for a while and consider wordplay to be an exercise essential to good health, you should be able to get it. If not, use the crossing letters to work out those answers with numbers in their clues, and then look at the cross-referenced answer.
I'll be back with the solution Monday. See you this weekend for Sunday brunch.
Link to puzzle: http://www.thenation.com/article/181893/puzzle-no-3340