Briggs and Stratton Intek Carburetor Solinoid

I have a  Briggs & Stratton, family YBXSX.5012VP   274826,   Engine Model 286H77-0165-E1  on a 2003 Toro Zero Turn mower.
 
I am replacing the carburetor solenoid and have a question.  When threading the solenoid (with right angle connector) into the bottom of the bowl, it is tight when the connector is facing the oil filter.   It is a very tight fit to plug in the cable, and I am worried about the wires close to the oil filter.     
 
Any ideas on how to reverse the orientation of the solenoid so the connection is more accessible?     Although I was trying to avoid removing anything more than necessary, should I remove the bowl from the carburetor and reverse it's orientation?   
 

Thanks - It is a Nikki -   There are two screws holding the bowl.     I may have to try that.     If not if I can tighten it just a little more I may be able to get the connector inserted - it is really tight. 
 
I appreciate the help!

Thanks -  I am not sure what carb was on the machine originally.   The shop replaced the carb a few years ago, and I suspect they used something from another engine.  That was the only time I had sent the machine out.    Over time the solenoid has gotten worse.  Feel like I am running out of gas - and mower stops.     Go back and tap the solenoid, reposition the connector, restart and good.   Very irritating.     Trying a replacement solenoid to see if that takes care of the problem.   If the carb is the issue, I may replace it with the Walbro based on your comment.