Your best bet is to call tracks in the area: tracks.kartpulse.com
Or find the nearest road course event near you. This topic has been updated with a calendar recently.
Generally a CR250 isn’t much faster (if at all) over a lap on a sprint course vs 125. It’s a more violent ride though 
Paddle shift should be worth some time though.
Otherwise you might have to see if a car or motorcycle series will let you tag along some day. Or save a bunch of cash and just rent a track all to yourself. These are both pretty involved as you can imagine.
I sympathize though, it sucks that you’re not able to find somewhere to stretch it’s legs just yet.
See if you can find some road racers from your way that travel, maybe share transport etc to an event like Mid Ohio?
Also. We need to see this kart… got any video?