Fred, I know you may take this suggestion as 'over the edge', but I would not rule out using that tower (paper, tho it is) to actually launch your model. I've had one out of balsa from back around 1970...
(see:
https://www.rocketryforum.com/showthread.php?19611-SCALE-Saturn-V-Gallery&p=568068#post568068 )
... and with the smallish motors used on a 1:100, even paper is not much at risk (on my LUT, the yellow 'blast deflectors' right around the flame opening is simply yellow painted poster board and even here (with AeroTech E motors + 4 mini-A outboards), there is, at most, just a little 'smoke flash'). It just doesn't hang around long enough to do any flame damage. Some slight re-engineering on the launcher platform (mine was 3/4" plywood painted gray) would probably all that would be needed. This model has seen literally dozens of launches and no damage past that 'smoke flash' has ever occurred. Since my tower is 'semi-scale', I'm thinking, instead of rebuilding a 'true scale' from scratch, just getting one of these paper models. I think one would be surprised how safe it would be in this application.
It's just some thoughts, but I wouldn't rule it out.
-- john.