OP -
No matter what carb you have, it will require tuning. Some are easier than others, but it will still take some tuning. Large changes in temperature, weather, or altitude will also take some tuning. So before you consider "upgrading" the carb, keep that in mind. I can say from first hand experience the stock oem carb on the XR650R can be made to work properly. I am not saying other carbs arent good, just that the oem can work as designed.
One of the reasons I asked some of the questions I did in my previous post is to get an idea and clues to your current jetting.
In the middle of day when its warmest outside and with a cold engine that has been sitting, does it require any choke to start? If so how much. 1/4, 1/2, full. If it requires full choke when its warm outside, your pilot or fuel screw setting might be too lean at night when its 30 degrees colder.
How many turns out your fuel screw is will also be a clue to your pilot jet. If its all the way out, your pilot may be too small and the bike is lean even with full choke. If its only out 3/4 a turn, it may be on the richer side and you may need a smaller pilot and the the bike is too rich with full choke at night.
No one can help until you can share these with us.
This is how I adjust a fuel screw on a 4t thumper. Bike needs to be fully warmed up to adjust the fuel screw, like ridden for 10-15 minutes. A few minutes idling is rarely enough. I don't like to adjust to a stumble and back off, I like to adjust to the highest idle and back off.
After the bike is fully warmed up, lower the idle with the idle adjustment screw until its barely running... lowest idle possible.
Turn the fuel screw in until the idles drops and or dies. If it doesn't when turning in, your pilot is too large and the bike too rich.
Next start turning your fuel screw out slowly until the idle increases. Continue turning out until the idle reaches it highest point (not until it stumbles as that is generally too rich.) Then back in 1/4 turn. Make a note of how many turns out from slightly seated it is.
If its more than three turns, you pilot might be too small, ie lean. Less than 3/4 turn, too large ie rich.
You can't do this properly with a high idle screw setting. To properly do this, its needs be barely running... you may even need to blip the throttle occasionally. Adjust the idle screw back to your preferred setting after adjusting the fuel screw.
The choke mechanism is pretty simple. In most carbs its merely a butterfly constricting air thereby enrichening the mixture (a few have a separate circuit controlled by a needle valve.) Easy to check its functionality when you pull the carb to verify what jets you have in the bike.
Why you have the carb out, may as well clean the jets. Soak overnight and put guitar string or something similar through the pilot to ensure its clear and clean if there is any question.
If the carb is functioning and tuned correctly and its still not starting when cold, then its time to look at other items like an air leak, valves, or even technique. Good luck