If the linkage is adjusted properly, then the problem is likely related to the reverse gear application in the transmission. Reverse gear uses a band to hold a drum from rotating. This band is applied by a servo (piston) that moves in a bore in the transmission case. If the servo is sticking or the seals on the servo are not properly in position, then the band can't apply properly and reverse gear doesn't engage properly.

The only disadvantage of synthetic oils is cost. If you decide you want to go back to synthetic oil at the next oil change because of different driving conditions, it isn't a problem. In my own vehicle I have switched between synthetic and conventional oils several times as I tested different types and brands of oil. Oil analysis has shown no problems with mechanical wear at any time, but I do notice the ease of starting in winter when using the same grade of synthetic as a conventional oil. If you want a lower cost and some of the benefits of synthetic, there are synthetic blends -- a mixture of conventional and synthetic oil that are available too.