If you’re really looking for a ‘large frame’ scooter, those are usually called maxis, and SYM and KYMCO both have them. They’re a little unhandy for putting around town, as they’re kinda long and heavy. Check out the galleries at their Taiwan sites to see what they have currently, or head down the shops. If you’re looking used, Yamaha used to make the Majesty in 125 and 250, but I haven’t seen it on their site for a couple years and don’t think they sell it anymore.
If you really want a 125 or 150, some of them have a surprising amount of legroom. Most don’t. There has been a trend lately for the manufacturers to put these little ‘steps’ on the floorboards of their smaller bikes, likely because the fuel tank has been relocated to the front, which gives better front/rear weight distribution but which is, I’m sure, because they are obsessed with getting as much stuff as possible under the seat. Look at this Yamaha GTR, for example:

This may be something that doesn’t matter to anyone else in the world, but on my older scoot, I can move my feet forward just by sliding, and not picking them up. This gives me seemingly more legroom. Of course, you’re still going to be pretty tied up on a small scoot, but I think the older kind with the smooth area in the front of the floorboards are more comfortable for taller people. I’m 183 cm and 34" legs.

And no, I don’t recommend buying an SVMax unless you can get it for NT20,000
You might look at the KYMCO G5 or SYM midsize (don’t know model names for them). The G5 125 has 10" wheels and is lighter; the 150 has 12" wheels. They’re both a 4 valve head, but I’m not sure if it’s the same 4 valve head.
I’d just go down the shops and see. There was also a bike called the Techno (SYM, I think) that’s somewhere in the middle as far as size goes. They didn’t sell very well, but you might be able to find a used one. Then there are the usual sport models: Yamaha Cygnus, KYMCO Racing, and SYM Fighter. Bigger than what I like, but they might interest you. Good luck.