Erik,
I would go first for the yagi for sure, but I want to point out the importance of the receive pre-amplifier on the amp. An amp like this isn’t just about getting louder, it is also about hearing better.
Chances are when you connect your 818 to your antenna if the background noise level is not enough to move your s-meter you may be able to benefit from a receive preamplifier. Noise levels can be really low on a summit so these are sometimes good places for preamps. A good preamp in the right conditions will take someone you can tell is there but can’t understand and turn it into a contact you can make.
I know my 817 and 706MKIIG are not particularly sensitive on 2m and are somewhat deaf on 70cm regardless of what the official stats say and they benefit from external mast mounted preamps on summits. 706MKIIG’s built in preamp simply isnt enough.
So definitely improve your antenna first (improve gain AND height --benefit to get above treetops), then examine your coax with a proper analyzer for loss and replace if necessary, then get an amplifier with a preamplifier as the final step.
I was shocked to see my RG-58 way out of spec on 2m when checked for loss with the MFJ analyzer. I had mistreated my RG-58 for too long (tight wrapping circles on a well known wire wrapper). I gained more than 3 db of signal on receive and TX just by moving to new and slightly larger coax.
If you want to go completely crazy, get a mast mounted preamplifier right by the yagi above the treetops AND a power amplifier by your rig on the ground. Oh and go to something like LMR-600UF for coax if your run is like 50 feet. Of course this all weighs allot!
As a final word, in the US at least on 2m SSB you can pretty much count on the station at home to be running something monstrous…if you can get your antenna above the treetops and the chasers know to look for you they will turn their massive array your way and blow you away regardless of what you are running. I worked K1TEO once on 2m SSB from a summit in Connecticut WHEN I HAD FORGOTTEN TO CONNECT THE COAX TO THE RADIO. He worked me with no antenna on my 817 during the ARRL VHF contest. Who knew all that coax and antennas were actually unnecessary 
73,
Tom, N2YTF