You can use VK1OD's online Transmission Line Loss Calculator to check the loss of
different types of coax, and a lot more:http://vk1od.net/calc/tl/tllc.php
RG-8x has 1.6dB loss in 150 feet when matched, so 2/3 of your power gets radiated.
That's acceptable for a lot of purposes, but the losses will be even higher than
RG-213 at a high SWR. But still, the losses will be several dB higher using low-loss
LMR-400 matched at the shack than RG-8X matched at the antenna, so that gives
you an idea of where you'll get the best return for your investment.
(You'll find RG-8X listed as Belden 9258 in VK1OD's calculator, since it is NOT a
MIL-STD designator and there are no standards for it across manufacturers.)
Here is VK1OD's evaluation of feeding options:http://vk1od.net/antenna/multibandunloadedvertical/index.htm
Any impedance can be matched using an "L" network using one coil and one
capacitor (though some loads may match easier using two capacitors or
two coils.) Often a single series or shunt coil or capacitor can get the SWR
low enough (perhaps below 5 : 1 or so) to keep losses reasonable on the
coax. The required value will be different on each band, so some sort
of switching is required.
When I put up an antenna at home that I expect to be using for an extended
period of time, I build a switched tuner for it. I have a chassis with a big
switch and a chunk of coil stock mounted on it. By experiment I find what
value of coil and capacitor are needed to match the antenna on each band,
then wire up the switch to select the required coil tap and fixed capacitor.
Then when I want to change bands I just turn the switch - instead of having
to adjust the tuner controls, they are preset to the right values. A similar
approach can be used with relays or a remote switch of some sort (or, if
you don't change bands often, a manual switch at the base of the antenna)
that gives you the function of matching at the antenna feedpoint for less
cost than a wide-range auto-tuner.