You have done the common fixes to keep it in 3rd gear. The side cover is only one component and I'm not sure the scissor type is going to help in this situation. If the 2-3 shift fork is good then the only other variable is a worn 2-3 syncro assembly. Take a look at the large ring on the 3rd gear end, (where the shift fork rides) if it is worn excessively the syncro is toast. If it is OK then the problem is worn syncro rings or the nubs that engage the energizer spring.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine