Sounds like the shifter base has to move slightly to the left.
The underside of the shift lever rides up against the lockout plate tab until either you push down on the (stock) lever or disengage/move the reverse lockout detent pin by pushing a button or pulling on the "reverse" lever. When that happens the lever is allowed to move farther to the left, but the part under the floor is allowed to move farther to the right. Yours is already too far over there.
There are three shifting forks inside of the transaxle nosecone and each does two gears by pushing in or pulling out from neutral: In order; 3/4, 1/2 and reverse (pull out).
Your problem is that you're already mostly over to where reverse is when you pull into second, but the lever still has some play in that direction and can "find" the reverse fork and pull it out and engage reverse gear. You are probably not centered on the reverse fork when that happens, and you're probably trying to engage BOTH second and reverse at the same time (it's possible, but the Transaxle really doesn't like it). You have to angle the shift rod back just a skosh to get it lined up properly for second. Believe me, it doesn't take much base movement to make a big difference.
As I mentioned way up above, loosen both base bolts a little but still kinda firm. Scribe along the base on the right side so you'll have a reference line drawn along the tunnel, right beside the base. Take a piece of hardwood and put it against the right side of the very bottom of the base and give it a smack or two with a hammer. You want it to move to the left 1/16"-1/8", both front and rear equally, so you don't want it too loose, just enough to resist the hammer blows but just enough to move slightly when hit, too.
If I understand correctly and you have another adjuster at the coupling just before the transaxle (and why would you need THAT? To me, that just complicates things) and if the shifter base will not move farther to the left, you'll need to adjust at the coupling to rotate the shift rod a degree or two to the left (driver's side) to accomplish the same thing.
Hope this helps.