Ah, Grasshopper, you’ve chosen the path less traveled...
A proper tube fin rocket most commonly has 6 ( or occasionally 7 ) fins which gives each tube fin three contact surfaces for attachment and the tubes support each other.
In spite of this, tube fins still occasionally break or break off in the landing.
“Salami” slicing the bottom of the tube fins can help by reducing the moment arm at impact and also reduce the normal landing damage to the outside edges of the tubes. ( Tube fin rockets NEVER stick the landing. )
BTW, CA glue is very brittle but epoxy has a bit of flex. Just saying.
You could also cut extra tube fins in half lengthwise and laminate them inside the tube fins with epoxy for extra strength in the manner of doublers.
Here’s one of mine in action last week. Note how short the tube fins are. This was an attempt to fool with the aspect ratio and produce a very straight boost with minimum drag. Mostly successful. 3” diameter tubing used for body and fins. Boost is on G77R and aimed away from downwind pond. Has flown on H165R motors also ( 18G’s off the pad! ). Red motors for red rockets, right? Multiple repairs to fins over the years but it keeps on going.
In spite of all these idiosyncrasies, tube fin rockets are cool and draw a lot of comments.