What you are looking for is a big bore 125 (134cc or 144cc) , not a long stroke engine.
It's pretty rare to increase the stroke on a 125 but big bore conversions are common, very reliable and most of all FUN! Basically the cylinder is over-bored to the new big bore size, and the cylinder ported for more low/mid, more mid/top, or an overall broader powerband. The head is esurfaced and machined for proper squish clearance and the bowl shape is re-contoured to accommodate a choice of fuel; pump or race gas.
Then the bore is re-plated with nickel silicon-carbide composite plating and Diamond honed to final size.
It's a fun and reliable package that has been used for exactly what you described for the last 10-12 years.
Eric Gorr at Forward Motion is innovator behind most of the big bore two-strokes that have been developed over that time. here's some info from his website :
http://ericgorr.com/bbmasterlisthtml.html
I spent a season on one of Eric Gorr's early development big bore 125s and I had a blast. I was 225lbs in gear at the time and it had more that enough torque to keep me amused all day long. They have only gotten better since then. You'll love the end result.