I'll mention a couple of things.
Try hard to visit a 13' and a 16' and get inside to see how it "fits". Best way is to find an Egg gathering near you so you can sample a number of rigs. You really won't know until you try. Or can you get to the Casita
factory? Both Scamp
maintain lists of owners willing to show their eggs at home.
I have doubts that the tongue weight
allowed on your S70 is the correct figure; I would treat it as a possible error until you can get it confirmed (Letter to them or check OM's for other years).
I would also look at the GCWR, the combined TV+Egg weight
allowed, to see what kind of cargo problems you might have.
Finally, the 16's don't weigh all that much more than the 13's IF you are ruthless in what you don't take along, esp stuf like an a/c and a shower/bath (the extras required for a bath not only cut down on space, they weigh a lot, what with more need for water, more need to hold waste, hot water heater [another 5-6 more gallons, plus LP]). What I'm trying to say here is that if a 13' is too small then perhaps a 16' with bath is also too small and also weighs more.
As Roger said, longer trailers are easier to back (and shorter overhangs [distance from rear axle
to hitch ball] on TV also make it easier).