... for 'base support' I'd make up two 3/8" > 1/2" thick x Width of your LT, + 2", either- side, aluminum 'rails', and use 'heavy'
(5/16" min; 3/8" better...) threaded-rod + double-nuts, top/bottom to make a 'box-clamp' around it, if you're just looking to prevent 'flex'...
IF you need to 'hang' from the base, this can be 'tied-in' to the 'pipe' design, up-top, ie:...
...Use your 'imagination', but do anything with at
least 5/16" min; 3/8" better, 1/2"-thick,
best, stock... Make a trip to your local Pro-audio / lighting shop and think 'hardcore'...
(I would not really recommend 'off the shelf' proj-brackets, etc...)
Hope this helps...
peace...
j