Dec 13 - 18 is right after National Finals Rodeo and before the xmas rush and is typically one of the low seasons/cheapest times to visit Vegas (and one of my favourite times to visit). I suspect you'll be able to find reasonable minimum table limits at a few casinos.

Our friends stayed at the Monte Carlo a few years back and they thought it was ok. I'd probably consider booking it if I could find it for under $60/night. What did you read that's giving you second thoughts?

That said, I'd probably prefer to stay at Planet Hollywood too; like the vibe better. NYNY and Paris might be within your spec too.
If you're not finding a room for $60/night, I think your cheapest options on strip in that vicinity are Bally's and Excalibur. I've stayed at them before too and while they're definitely not my favourites, the rooms are fine IMO and it's kind of easy enough to hop over to a more interesting neighbouring casino.

If you do the $20 trick, my suggestion is just be nice to the clerk and politely ask for a upgrade, if even a for a view of the strip instead of getting a default view to the parking lot.