99.9999% of shifting problems are related to the cable. I don't see your case as being any different. The friction front should make the use an any front derailer of any flavor simple. Using a 9 speed front or a 10 speed front derailer shouldn't make a lick of difference.

From what you describe, the cable doesn't have enough movement to pulling the derailer far enough outboard. This could be due to the inner cable being too slack (possible but not likely since it's been adjusted) or something it catching the inner cable and preventing it from moving far enough. I would suspect the latter.

SIS outer cable can break down and the rods that make up the cable can come loose. Shift the bike into as high a gear on the front as you can then downshift without pedaling. This will release tension on the inner cable and give you some slack. Pull the cable housing out of the stops and take a look at the ends. Perhaps even slide the ferrules off if you can. What you are looking for is this



Little bits of wire sticking out where they shouldn't be. Without the ferrule, it might look like this



Another possibility is that the cable housing has been trimmed like this



This is something that manufacturers do all the time and I can't understand why. When you pull on the shifter, the rods in the cable housing bend inward and clamp around the inner cable. Since shifting to the largest ring requires the most tension, the clamping around the inner cable is worst for those shifts.