Colin looks good and looks...... familiar
Suggestion: Since your tank's longer than mine, I would put in additional cross planks (two 2x6s) in between whats there now. I would do this because you are using melamine base which is really just particle board. Any concentration of heavy weight in between those cross planks will cause the melamine to flex (this may occur when going up or down stairs). The main concern is that the flexing will cause the melamine to crumble around where the screws are located causing the melamine to break away from the 2x6 platform - not so bad if you are on flat ground but could be pretty inconvenient if halfway up the stairs.
Then I would do what you asked about putting a 2x4 on the sides but I would go with 2x6 and make sure you put a couple of 2.5" - 3" screws on each of the ends of the cross planks and every 6 inches along the long planks. The 2x6 will also serve to brace the sides of the tank from sliding.
That should make the sleigh pretty strong and reinforce the horizontal support.
Good luck.