There are two adjustments, the main one at the transmission(DTRS), and the indicator in the dash. The main cable adjustment should be what you need to work with to correct the starter engagement issue.
The dash indicator is relatively easy to adjust. There is a tiny vertical screw/bolt(5.5mm I think) under the column on the right side of it which holds it on, and a thumb wheel adjuster that rotates horizontally. I don't know if you can get to it without removing the knee cover pieces, so look first. Look straight up under the area where the key goes, the thumb wheel piece is white I believe.
I'd adjust that first, and expect it to not help the starter circuit. The DTRS(range sensor) is bolted to the shift lever at the trans, and has an adjustment mark on it. I forgot where the trans has to be to bolt the DTRS on, I'd say you can tell by carefully watching what gear it's closest to while loosening the bolt. Basically the trans is placed into the proper position with the shift lever of the transmission, and the DTRS is loosely placed on it, and the mark lined up, and then bolted tight.
It sounds like yours is just off a hair from where that DTRS adjustment is supposed to be. This is all done at the trans, not inside, so pull the battery cable off and turn the ignition on to unlock the column. So find the marks on the DTRS, and the other part adjacent to that.
Move the shift lever and watch that mark, to locate the other mark or shape it needs to line up with. Get it close to lining up, most likely it'll be off a hair and won't line up perfectly(you will feel the shift lever at the transmission, move from each gear to the next). Loosen the bolt that locks the DTRS down, and move it the small amount it needs to, to line up the two marks. Tighten the bolt wrist tight, and then gently run the shift lever through all positions. Then check the shifter on the column to see that it also reaches all positions.