Instead of trying to get 100 watts for SSB on 11 meters, why not do what you are supposed to do in Amatuer Radio. Use the least power needed to maintain reliable communication so that you do not interfere unnecessarily with others. If you can make contact with 12 watts PEP using SSB, the only reason you would want to use 100 or 1000 watts would be to talk over someone which is what happens on 11 meters all the time.
Ever hear of QRP radio? Typically 10 watts PEP or less on SSB for HAM radio. Lots of HAM radio operators make plenty of contacts around the world with just that. Legal 11 meter SSB radios are allowed 12 watts PEP.
If mobile, a full length quarter wave vertical whip and a good ground to the vehicle is as good as a quarter wave ground plane at the same height above ground for line of sight. For atmospheric hops (skip), antenna elevation is usually unimportant.
When I was a teen back in the 70s, I wish I had know some of what I know now as a HAM. I could have amazed other CBers using a simple inverted V antenna for DX. I never used more than the CB could do with 4 watts AM. A neighbor had a 500 watt linear amplifier and a quarter wave ground plane in the top of a 60 foot pine tree only doing AM mode. Had I known then as much as I do about propagation and antennas now, I could have beat his DX reach.
Point is, use the 12 watts PEP with a good antenna for DX, and when the band is open be amazed what you can do. A quarter wave ground plane is not the best choice for DX. Anything you can learn about Inverted V, horizontal dipole, long wire, sloping long wires for 10 meters is applicable for 11 meters. The length of the elements are just a bit longer.