There are plenty of advisors on the ground.
I wonder if you have any idea of the bells that phrase rings? Vietnam started with advisors and ended with an army of conscripts defeated by little men with bicycles.
...let the ground forces finish them.
What ground forces? Assad has no need to send in ground forces to deal with ISIS that are being bombed "day and night". His priority is defeating the Free Syrian Army and the rest of the Syrian opposition. Putin wants his Mediterranean Bases so that he can assert his power there, and can do so as long as Assad is in power. The Kurds I grant are fierce fighters, but their ambition is for a Kurdish Nation, and once they have seized that territory their interest in rescuing those such as the American woman you instance will be marginal. This is Real Politik, and the UK should only go to war if it cannot be avoided and if it can win. Win what? I ask again, what is the aim?