I had trouble matching until I built a gamma with a tube somewhere around 17" long x 3/4" diameter with a rod 30" long. It was dicey finding a working relationship between the rod extension amount and the strap from the vertical to the rod location. Once found it did a great job over a significant bandwidth.
Homer, I read in your link on the "Vector 4000 Remake" saying you did not know the dimensions for the gamma match.
You were probably asking the wrong guys...I had this info back then.
I'm can't be sure about those dimensions working, because the info was from somebody else. I did know a little about the LW150 antenna from a neighborhood CB buddy that had two old Sigma styled antennas back in the day, long before I ever heard about Siro. I never owned a Vector however, but I did buy 3 Vector knockoffs for other guys on the radio and I've posted that story on WWDX before.
I tried a 7/8^ length, but believe I backed it down to 3/4^ (27'6") for my best results.
I don't recall you trying a 7/8 wave radiator. I just recall your antenna might have been longer than the stock Sigma4/NV4K. Until now...I never knew for sure. Same goes for Booty Monster.
I tried the same thing making my A.S. Sigma4 about 2' feet longer and I could not get a match anywhere within the full range of the stock gamma match...which wasn't much.
My gamma dimensions:
Base is 1/2" x 10" inches
Rod overall is 38" x 3/16" inches
Rod to dog bone exposed is 22" inches above top off base tube
Dog bone from feedpoint is 32" inches
I could make no tuning progress with the radials attached against the vertical with no standoff.
I seem to remember us talking about that too. I've said before, this offset may also be necessary in such a real world antenna. However, I think I read in your V4 Remake thread, that your first or second V4K/G4 antenna with this design that worked really well...had the radials connected directly to the mast, (I could be wrong though).