I'm no pro, and I'll admit I'm biased towards wanting more legal stages, but I actually feel like the 3DS has a number of viable stages. I'm not going to try to separate into Starter/Counterpick, but I think these stages could be competitively viable:
Tortimer Island
Find Mii
Arena Ferox
Reset Bomb Forest
Rainbow Road
PictoChat 2
Prism Tower
Boxing Ring
F-Zero SNES
Spirit Train
Tomodachi Collection
Gaur Plain
Battlefield
Final Destination
Yoshi's Island
All Omega Versions
A lot of these may be controversial, but judging from what I've seen, I believe it is perfectly possible to have a fair fight on pretty much all these stages, unless there's something gamebreaking I'm missing about any of them.
And to prevent oversaturation of FD, the way I'd do stage selection after a first match would be that the loser of the previous match would be able to choose that he wants an Omega stage, and then the other player has the opportunity to pick which Omega stage. That way, they're more or less treated as a single stage.
I'm going to copy your list and put the pros/cons I perceive for each. I generally agree across the list, but I can see some valid reasons.
Tortimer Island
Pros - Variable layout, water non-swimmable, no walkoff, no circlecamp, one very obvious and offstage hazard
Cons - Items from trees may be considered a con by some players, though I find it just opens item play to more characters than those who make their own. Boat can carry people off the side. Hazard exists.
Find Mii
Pros - Distinct platforms, unique layout
Cons - Large and powerful roaming hazard which can remove terrain for a long period of time. Floating solid cage. Narrow recovery tube biased towards wallkicks and against Ness. Unclear stat bonus properties.
Arena Ferox
Pros - Neutral form. Variable platform configurations encouraging shifting playstyles. Fire Emblem stage (personal bias)
Cons - Statues arguably block projectiles and attack hitboxes. Solid walls can cause fightclubs and camping like Pokemon Stadium 1
Reset Bomb Forest
Pros - Standard platform configuration in mode 1. Predictable hazard
Cons - Breakable platforms in mode 2. Hazard. Maybe largeish in mode 2 (don't have JP copy to test myself)
Rainbow Road
Pros - Versatile platform configurations
Cons - Occasional walkoffs. Shy Guy hazards. Some stops lack a clear main platform
PictoChat 2
Pros - Versatile platform configuration. Simple base form
Cons - Lots of damaging or physics-altering hazards.
Prism Tower
Pros - Versatile platform configuration.
Cons - Temporary walkoff. Induces motion sickness (personal issue)
Boxing Ring
Pros - Unique terrain layout. Ropes introduce a new means of aerial approach
Cons - Permanent walkoffs. Light hazard. Ceiling KO potential from lights. Ability to camp lights away from some characters entirely.
Mute City
Pros - Unique and nonstatic platform layout.
Cons - No bottom blast zone. Cars MIGHT be randomly timed (haven't seen enough to know).
Spirit Train
Pros - Variable platform layout
Cons - Shifting platform position relative to blast lines. Explosive hazards. No bottom blast line.
Tomodachi Life
Pros - Flat and Plat.
Cons - High chances of ceiling KO at high platforms. Some concerns of circle camping.
Gaur Plain
Pros - Unique platform configuration.
Cons - Few large platforms. Permanent walkoffs.
Battlefield
Pros - Flat and plat.
Cons - Platforms can interfere with vertical projectiles.
Final Destination
Pros - Flat.
Cons - Very long
Yoshi's Island
Pros - Slightly not-flat. Single predictable platform.
Cons - Random ghost platforms. Shyguys block projectiles.
All Omega Versions
Pros - Flat. Variable stage undersides.
Cons - Long (but is it variable compared to the default FD or are they all the same?)