My only concern is that the antenna is close to resonant on 30m, and a quarter wave of
line (about 20 feet or so) may step the impedance up to an inconvenient value. A quick
model suggests the SWR on 300 ohm line is only 4 : 1, so the maximum impedance you
would encounter is 1200 ohms. That's probably tolerable.
Here is one way you can check the values yourself:
W9CF has a handy yagi modelling applet you can run online here:http://fermi.la.asu.edu/w9cf/yagipub/index.html
Create a single element yagi with a 50' element (using perhaps 25 segments for good
measure) and see what feedpoint impedance it gives you for each band.
Then you can stick the impedance into VK1OD's transmission line loss calculator here:http://vk1od.net/calc/tl/tllc.php
for various lengths of 300 ohm line and see what the resulting impedance is at the tuner.