Frankly I don't think 10W will drive any linear to 1kW.
You will get the most gain from a Tetrode but I still
don't think it will go 20db. I suggest you search for
richard measures web page and read some of his articles
about the merits of GG vs grid driven amplifiers.

I think you will need an intermediate stage to get
enough drive. Then you might as well pick up an old
Heath SB200 or SB220 for the final stage.
The SB200 will give you 500-600 watts out with a
pair of 572s and you can buy them for 300 bucks.
Plus the tubes are not too expensive if you need new ones.

chuck