Do I merge either or both of the small companies with the large company knowing I cannot get any more stock in the big company because it is no longer available?
Can you get more stock in the small companies? Can your opponents?
If you cannot and they can, then you want to merge now to end the game rather than letting them buy more stock (whose value may increase). Unless you believe the others who have cash and can buy more are not your serious competitors anyway (i.e. they'll finish behind you in any case). Then you'd rather let the game continue and increase the size of the chain - assuming you own more stock in it than your serious competitors.
Do I just hang on to the stock and not merge the companies so I can get the value of the stock at game end for the two smaller companies?
You get the value of your stock either way (whether it merges or whether it's game over).
Do I merge the companies and hope that I will profit as the majority or minority holder because the bonus will be worth more than the stock will be at game end?
That dichotomy doesn't make sense; you get the value of the stock either way (whether it merges or whether it's game over), and you get the majority holder bonus if you deserve it either way (whether it merges or whether it's game over).
Will the stock at game end, which will be soon, be worth more than merging and selling the stocks for cash since there is no more stock to buy?
Only if the chains can grow larger so that the price goes up. That's usually pretty easy to see if they have room to grow or not.