That's a tall order.
I'd suggest putting priorities on which of those is most important to you, because you aren't going to find all that in a single reactor. I responded to a much less ambitious request that also was unfortunately not possible with proof here http://forum.industrial-craft.…ad&postID=42434#post42434.
I'll pull out some highlights, and link them up to your requests.
-Can have external water cooling
I generally assume this, it is factored in to remaining designs.
-Can NOT be a CASUC
This allows for 6 chambers, and eliminates SUC as even a stack of ice is inferior to a cooling cell.
-MUST be AT MOST a MK2
128 heat generated is over the maximum for mark II. At that heat and above, parts melt before cycle completion
-Cooldown MUST be below 30 seconds
73 heat generated is over the maximum for mark I (30s cooldown is approaching mark I). Above that and parts need time to cool down
-Must be HV or EV
this design constraint is confusing. HV is 512 eu/p. Reactors put out whatever eu/p they generate, a factor of 10. You may not need to make this a design constraint if you have a transformer on the reactor output it will just convert power to the voltage of your choice. If you need to make the reactor spit out 512 eu packets, it ain't gonna happen. Have it spit whatever sized packets into and HV/EV transformer and you get 512/2048 eu packets out.
-Efficiency 3 or more
4u in a square is the smallest config of u that generates energy efficiency 3. Surrounded by appropriate cooling, that is 96 heat generated. This exceeds your mark I requirement (or Mark II - e). 6u in a rectangle is the minimum u config to get > 3 energy efficiency @ 3.33 efficiency. It generates 176 heat, and thus cannot even be a mark II.
Duezman's efficiency 3 mark II is the best (lowest cooldown, highest eff eu/t).
http://www.talonfiremage.pwp.b…4k87s7mw1b5s3rmkfdlebhmv5
Efficiency 3 will absolutely require a cool down period. Greater than 3 efficiency will require you to bust out your redstone skills on setting up a timer.
With current available parts limiting mark I designs to well below the heat required for efficiency 3 uranium consumption, you have to pick between more uranium consumed or more time & risk taken to get the same energy. Of course it's easy to demand both, but design forces a trade off.