This is good news except for the no squirt part

To be sure I understand what you have done, I am going to restate in my own words, please confirm if correct: By jumping out the relay you have confirmed its pumping gas all the way up to the carb. Correct?
Now did you leave it running for 30 or 45 seconds (heck can just leave it running) and then stroked the throttle looking for a squirt?
- This is the part that I am usure of > did you provide enough time to fill the carb float bowl back up (vs just ‘fill the line’)? Hopefully my question make sense.
Here is a vid I found showing the squirt to look for
link. If indeed you do not have a squirt, then its carb rebuild time.
Also, does not matter throttle lever forward or reverse, the carb only knows closed to open back to close. You may have noticed there was no difference in movement of the linkage at the carb regardless of moving the throttle lever fwd or reverse.